WEBVTT
Kind: captions
Language: en

00:00:04.310 --> 00:00:07.519 align:start position:0%
 
in<00:00:05.310><c> the</c><00:00:05.460><c> last</c><00:00:05.609><c> film</c><00:00:05.910><c> we</c><00:00:06.480><c> looked</c><00:00:06.690><c> at</c><00:00:06.839><c> variations</c>

00:00:07.519 --> 00:00:07.529 align:start position:0%
in the last film we looked at variations
 

00:00:07.529 --> 00:00:09.680 align:start position:0%
in the last film we looked at variations
in<00:00:07.710><c> people's</c><00:00:08.099><c> weight</c><00:00:08.400><c> and</c><00:00:08.730><c> discovered</c><00:00:09.570><c> that</c>

00:00:09.680 --> 00:00:09.690 align:start position:0%
in people's weight and discovered that
 

00:00:09.690 --> 00:00:11.780 align:start position:0%
in people's weight and discovered that
we<00:00:09.780><c> could</c><00:00:09.809><c> represent</c><00:00:10.230><c> a</c><00:00:10.710><c> whole</c><00:00:10.920><c> population</c><00:00:11.700><c> of</c>

00:00:11.780 --> 00:00:11.790 align:start position:0%
we could represent a whole population of
 

00:00:11.790 --> 00:00:14.870 align:start position:0%
we could represent a whole population of
people<00:00:11.969><c> by</c><00:00:12.570><c> a</c><00:00:12.599><c> normal</c><00:00:13.110><c> distribution</c><00:00:13.849><c> we</c><00:00:14.849><c> can</c>

00:00:14.870 --> 00:00:14.880 align:start position:0%
people by a normal distribution we can
 

00:00:14.880 --> 00:00:16.880 align:start position:0%
people by a normal distribution we can
explore<00:00:15.480><c> more</c><00:00:15.630><c> the</c><00:00:15.690><c> statistics</c><00:00:16.289><c> of</c><00:00:16.410><c> many</c>

00:00:16.880 --> 00:00:16.890 align:start position:0%
explore more the statistics of many
 

00:00:16.890 --> 00:00:20.210 align:start position:0%
explore more the statistics of many
phenomena<00:00:17.520><c> using</c><00:00:17.910><c> this</c><00:00:18.060><c> concept</c><00:00:19.010><c> if</c><00:00:20.010><c> we've</c>

00:00:20.210 --> 00:00:20.220 align:start position:0%
phenomena using this concept if we've
 

00:00:20.220 --> 00:00:22.040 align:start position:0%
phenomena using this concept if we've
measured<00:00:20.430><c> the</c><00:00:20.609><c> diameter</c><00:00:20.880><c> of</c><00:00:21.330><c> all</c><00:00:21.600><c> the</c><00:00:21.810><c> trees</c>

00:00:22.040 --> 00:00:22.050 align:start position:0%
measured the diameter of all the trees
 

00:00:22.050 --> 00:00:24.070 align:start position:0%
measured the diameter of all the trees
in<00:00:22.080><c> the</c><00:00:22.380><c> wood</c><00:00:22.560><c> and</c><00:00:22.800><c> then</c><00:00:23.100><c> plotted</c><00:00:23.760><c> that</c>

00:00:24.070 --> 00:00:24.080 align:start position:0%
in the wood and then plotted that
 

00:00:24.080 --> 00:00:26.349 align:start position:0%
in the wood and then plotted that
information<00:00:25.080><c> as</c><00:00:25.230><c> a</c><00:00:25.260><c> frequency</c><00:00:25.740><c> distribution</c>

00:00:26.349 --> 00:00:26.359 align:start position:0%
information as a frequency distribution
 

00:00:26.359 --> 00:00:30.109 align:start position:0%
information as a frequency distribution
what<00:00:27.359><c> would</c><00:00:27.480><c> it</c><00:00:27.570><c> look</c><00:00:27.689><c> like</c><00:00:28.429><c> it</c><00:00:29.429><c> would</c><00:00:29.640><c> conform</c>

00:00:30.109 --> 00:00:30.119 align:start position:0%
what would it look like it would conform
 

00:00:30.119 --> 00:00:32.450 align:start position:0%
what would it look like it would conform
to<00:00:30.480><c> something</c><00:00:30.960><c> like</c><00:00:31.140><c> a</c><00:00:31.199><c> normal</c><00:00:31.800><c> distribution</c>

00:00:32.450 --> 00:00:32.460 align:start position:0%
to something like a normal distribution
 

00:00:32.460 --> 00:00:36.260 align:start position:0%
to something like a normal distribution
you<00:00:32.730><c> have</c><00:00:33.480><c> a</c><00:00:33.600><c> few</c><00:00:33.899><c> very</c><00:00:34.079><c> small</c><00:00:34.200><c> trees</c><00:00:34.920><c> a</c><00:00:35.270><c> few</c>

00:00:36.260 --> 00:00:36.270 align:start position:0%
you have a few very small trees a few
 

00:00:36.270 --> 00:00:39.619 align:start position:0%
you have a few very small trees a few
very<00:00:36.690><c> large</c><00:00:37.140><c> ones</c><00:00:37.380><c> and</c><00:00:38.030><c> lots</c><00:00:39.030><c> and</c><00:00:39.270><c> lots</c><00:00:39.450><c> of</c>

00:00:39.619 --> 00:00:39.629 align:start position:0%
very large ones and lots and lots of
 

00:00:39.629 --> 00:00:39.979 align:start position:0%
very large ones and lots and lots of
them

00:00:39.979 --> 00:00:39.989 align:start position:0%
them
 

00:00:39.989 --> 00:00:43.819 align:start position:0%
them
somewhere<00:00:40.950><c> in</c><00:00:41.040><c> between</c><00:00:42.290><c> we</c><00:00:43.290><c> can</c><00:00:43.469><c> use</c><00:00:43.649><c> these</c>

00:00:43.819 --> 00:00:43.829 align:start position:0%
somewhere in between we can use these
 

00:00:43.829 --> 00:00:45.830 align:start position:0%
somewhere in between we can use these
principles<00:00:44.070><c> to</c><00:00:44.670><c> consider</c><00:00:45.120><c> the</c><00:00:45.539><c> probability</c>

00:00:45.830 --> 00:00:45.840 align:start position:0%
principles to consider the probability
 

00:00:45.840 --> 00:00:50.029 align:start position:0%
principles to consider the probability
of<00:00:46.289><c> shares</c><00:00:46.710><c> making</c><00:00:47.219><c> a</c><00:00:47.340><c> given</c><00:00:47.610><c> return</c><00:00:48.860><c> the</c><00:00:49.860><c> way</c>

00:00:50.029 --> 00:00:50.039 align:start position:0%
of shares making a given return the way
 

00:00:50.039 --> 00:00:51.319 align:start position:0%
of shares making a given return the way
in<00:00:50.129><c> which</c><00:00:50.280><c> wealth</c><00:00:50.579><c> and</c><00:00:50.850><c> income</c><00:00:50.940><c> is</c>

00:00:51.319 --> 00:00:51.329 align:start position:0%
in which wealth and income is
 

00:00:51.329 --> 00:00:54.049 align:start position:0%
in which wealth and income is
distributed<00:00:52.129><c> order</c><00:00:53.129><c> likely</c><00:00:53.430><c> intelligence</c>

00:00:54.049 --> 00:00:54.059 align:start position:0%
distributed order likely intelligence
 

00:00:54.059 --> 00:00:55.910 align:start position:0%
distributed order likely intelligence
quotient<00:00:54.570><c> of</c><00:00:54.629><c> any</c><00:00:54.840><c> person</c><00:00:55.410><c> or</c><00:00:55.590><c> group</c><00:00:55.620><c> of</c>

00:00:55.910 --> 00:00:55.920 align:start position:0%
quotient of any person or group of
 

00:00:55.920 --> 00:00:59.720 align:start position:0%
quotient of any person or group of
people<00:00:56.600><c> the</c><00:00:57.600><c> list</c><00:00:57.840><c> is</c><00:00:57.989><c> endless</c><00:00:58.170><c> the</c><00:00:58.730><c> normal</c>

00:00:59.720 --> 00:00:59.730 align:start position:0%
people the list is endless the normal
 

00:00:59.730 --> 00:01:01.670 align:start position:0%
people the list is endless the normal
distribution<00:01:00.359><c> is</c><00:01:00.840><c> one</c><00:01:01.289><c> of</c><00:01:01.410><c> the</c><00:01:01.500><c> most</c>

00:01:01.670 --> 00:01:01.680 align:start position:0%
distribution is one of the most
 

00:01:01.680 --> 00:01:06.850 align:start position:0%
distribution is one of the most
important<00:01:02.309><c> concepts</c><00:01:02.730><c> and</c><00:01:02.940><c> statistics</c>

00:01:06.850 --> 00:01:06.860 align:start position:0%
 
 

00:01:06.860 --> 00:01:09.800 align:start position:0%
 
shoplifting<00:01:07.860><c> is</c><00:01:08.369><c> a</c><00:01:08.430><c> problem</c><00:01:09.030><c> for</c><00:01:09.210><c> retailers</c>

00:01:09.800 --> 00:01:09.810 align:start position:0%
shoplifting is a problem for retailers
 

00:01:09.810 --> 00:01:13.340 align:start position:0%
shoplifting is a problem for retailers
everywhere<00:01:10.590><c> but</c><00:01:11.369><c> the</c><00:01:11.490><c> problem</c><00:01:11.909><c> is</c><00:01:12.360><c> not</c><00:01:12.900><c> taking</c>

00:01:13.340 --> 00:01:13.350 align:start position:0%
everywhere but the problem is not taking
 

00:01:13.350 --> 00:01:16.609 align:start position:0%
everywhere but the problem is not taking
one<00:01:13.590><c> once</c><00:01:14.010><c> one</c><00:01:14.549><c> pieces</c><00:01:15.000><c> a</c><00:01:15.150><c> one</c><00:01:16.080><c> piece</c><00:01:16.380><c> of</c>

00:01:16.609 --> 00:01:16.619 align:start position:0%
one once one pieces a one piece of
 

00:01:16.619 --> 00:01:18.590 align:start position:0%
one once one pieces a one piece of
merchandise<00:01:17.009><c> apparently</c><00:01:17.909><c> taking</c><00:01:18.270><c> the</c><00:01:18.390><c> whole</c>

00:01:18.590 --> 00:01:18.600 align:start position:0%
merchandise apparently taking the whole
 

00:01:18.600 --> 00:01:21.530 align:start position:0%
merchandise apparently taking the whole
stack<00:01:19.049><c> and</c><00:01:19.350><c> running</c><00:01:19.680><c> that's</c><00:01:19.890><c> all</c><00:01:20.420><c> you</c><00:01:21.420><c> know</c>

00:01:21.530 --> 00:01:21.540 align:start position:0%
stack and running that's all you know
 

00:01:21.540 --> 00:01:25.249 align:start position:0%
stack and running that's all you know
they<00:01:21.720><c> comment</c><00:01:23.000><c> every</c><00:01:24.000><c> retailer</c><00:01:24.720><c> suffers</c><00:01:25.110><c> from</c>

00:01:25.249 --> 00:01:25.259 align:start position:0%
they comment every retailer suffers from
 

00:01:25.259 --> 00:01:27.920 align:start position:0%
they comment every retailer suffers from
it<00:01:25.759><c> what's</c><00:01:26.759><c> often</c><00:01:26.970><c> happened</c><00:01:27.390><c> with</c><00:01:27.540><c> I</c><00:01:27.720><c> mean</c>

00:01:27.920 --> 00:01:27.930 align:start position:0%
it what's often happened with I mean
 

00:01:27.930 --> 00:01:29.780 align:start position:0%
it what's often happened with I mean
thieves<00:01:28.170><c> nowadays</c><00:01:28.619><c> is</c><00:01:28.860><c> you</c><00:01:29.009><c> steal</c><00:01:29.250><c> to</c><00:01:29.430><c> order</c>

00:01:29.780 --> 00:01:29.790 align:start position:0%
thieves nowadays is you steal to order
 

00:01:29.790 --> 00:01:31.670 align:start position:0%
thieves nowadays is you steal to order
and<00:01:29.939><c> you</c><00:01:30.420><c> will</c><00:01:30.570><c> find</c><00:01:30.810><c> that</c><00:01:30.990><c> you</c><00:01:31.110><c> lose</c><00:01:31.350><c> a</c><00:01:31.380><c> lot</c><00:01:31.650><c> of</c>

00:01:31.670 --> 00:01:31.680 align:start position:0%
and you will find that you lose a lot of
 

00:01:31.680 --> 00:01:33.890 align:start position:0%
and you will find that you lose a lot of
books<00:01:32.009><c> say</c><00:01:32.250><c> you</c><00:01:32.670><c> would</c><00:01:32.820><c> spot</c><00:01:33.090><c> that</c><00:01:33.390><c> and</c>

00:01:33.890 --> 00:01:33.900 align:start position:0%
books say you would spot that and
 

00:01:33.900 --> 00:01:35.300 align:start position:0%
books say you would spot that and
because<00:01:34.200><c> we</c><00:01:34.350><c> know</c><00:01:34.530><c> what</c><00:01:34.740><c> should</c><00:01:34.890><c> be</c><00:01:35.040><c> on</c><00:01:35.159><c> our</c>

00:01:35.300 --> 00:01:35.310 align:start position:0%
because we know what should be on our
 

00:01:35.310 --> 00:01:38.960 align:start position:0%
because we know what should be on our
shelves<00:01:36.799><c> news</c><00:01:37.799><c> agents</c><00:01:38.250><c> also</c><00:01:38.579><c> suffer</c><00:01:38.939><c> from</c>

00:01:38.960 --> 00:01:38.970 align:start position:0%
shelves news agents also suffer from
 

00:01:38.970 --> 00:01:41.359 align:start position:0%
shelves news agents also suffer from
shoplifting<00:01:39.360><c> people</c><00:01:40.350><c> come</c><00:01:40.590><c> in</c><00:01:40.770><c> steal</c>

00:01:41.359 --> 00:01:41.369 align:start position:0%
shoplifting people come in steal
 

00:01:41.369 --> 00:01:45.350 align:start position:0%
shoplifting people come in steal
magazines<00:01:42.020><c> newspapers</c><00:01:43.020><c> etc</c><00:01:44.090><c> how</c><00:01:45.090><c> do</c><00:01:45.149><c> they</c>

00:01:45.350 --> 00:01:45.360 align:start position:0%
magazines newspapers etc how do they
 

00:01:45.360 --> 00:01:48.440 align:start position:0%
magazines newspapers etc how do they
control<00:01:45.750><c> it</c><00:01:46.520><c> at</c><00:01:47.520><c> one</c><00:01:47.700><c> thing</c><00:01:47.820><c> they</c><00:01:47.970><c> can</c><00:01:48.119><c> do</c><00:01:48.270><c> is</c>

00:01:48.440 --> 00:01:48.450 align:start position:0%
control it at one thing they can do is
 

00:01:48.450 --> 00:01:50.649 align:start position:0%
control it at one thing they can do is
install<00:01:49.020><c> security</c><00:01:49.619><c> devices</c><00:01:49.950><c> like</c><00:01:50.310><c> this</c><00:01:50.490><c> one</c>

00:01:50.649 --> 00:01:50.659 align:start position:0%
install security devices like this one
 

00:01:50.659 --> 00:01:53.990 align:start position:0%
install security devices like this one
but<00:01:51.659><c> it</c><00:01:51.750><c> costs</c><00:01:52.340><c> and</c><00:01:53.340><c> so</c><00:01:53.490><c> whatever</c><00:01:53.670><c> they</c><00:01:53.939><c> do</c>

00:01:53.990 --> 00:01:54.000 align:start position:0%
but it costs and so whatever they do
 

00:01:54.000 --> 00:01:56.319 align:start position:0%
but it costs and so whatever they do
it's<00:01:54.600><c> going</c><00:01:54.750><c> to</c><00:01:54.810><c> reduce</c><00:01:55.020><c> their</c><00:01:55.380><c> profits</c>

00:01:56.319 --> 00:01:56.329 align:start position:0%
it's going to reduce their profits
 

00:01:56.329 --> 00:01:58.609 align:start position:0%
it's going to reduce their profits
preventing<00:01:57.329><c> a</c><00:01:57.420><c> discouraging</c><00:01:58.049><c> theft</c><00:01:58.409><c> is</c>

00:01:58.609 --> 00:01:58.619 align:start position:0%
preventing a discouraging theft is
 

00:01:58.619 --> 00:02:01.520 align:start position:0%
preventing a discouraging theft is
costly<00:01:59.479><c> businesses</c><00:02:00.479><c> respond</c><00:02:00.930><c> to</c><00:02:01.020><c> shoplifting</c>

00:02:01.520 --> 00:02:01.530 align:start position:0%
costly businesses respond to shoplifting
 

00:02:01.530 --> 00:02:04.459 align:start position:0%
costly businesses respond to shoplifting
in<00:02:01.680><c> many</c><00:02:01.890><c> ways</c><00:02:02.159><c> with</c><00:02:02.549><c> security</c><00:02:03.479><c> systems</c><00:02:03.869><c> with</c>

00:02:04.459 --> 00:02:04.469 align:start position:0%
in many ways with security systems with
 

00:02:04.469 --> 00:02:07.370 align:start position:0%
in many ways with security systems with
item<00:02:04.979><c> tags</c><00:02:05.280><c> and</c><00:02:05.610><c> with</c><00:02:06.299><c> trained</c><00:02:06.719><c> staff</c><00:02:07.079><c> and</c>

00:02:07.370 --> 00:02:07.380 align:start position:0%
item tags and with trained staff and
 

00:02:07.380 --> 00:02:08.520 align:start position:0%
item tags and with trained staff and
surveillance

00:02:08.520 --> 00:02:08.530 align:start position:0%
surveillance
 

00:02:08.530 --> 00:02:11.190 align:start position:0%
surveillance
even<00:02:09.220><c> University</c><00:02:09.850><c> Libraries</c><00:02:10.390><c> lose</c><00:02:10.660><c> books</c><00:02:10.990><c> to</c>

00:02:11.190 --> 00:02:11.200 align:start position:0%
even University Libraries lose books to
 

00:02:11.200 --> 00:02:11.840 align:start position:0%
even University Libraries lose books to
thieves

00:02:11.840 --> 00:02:11.850 align:start position:0%
thieves
 

00:02:11.850 --> 00:02:14.970 align:start position:0%
thieves
in<00:02:12.850><c> response</c><00:02:13.390><c> this</c><00:02:14.020><c> library</c><00:02:14.290><c> has</c><00:02:14.590><c> installed</c>

00:02:14.970 --> 00:02:14.980 align:start position:0%
in response this library has installed
 

00:02:14.980 --> 00:02:17.460 align:start position:0%
in response this library has installed
electronic<00:02:15.790><c> item</c><00:02:16.120><c> tanks</c><00:02:16.540><c> and</c><00:02:16.690><c> electronic</c>

00:02:17.460 --> 00:02:17.470 align:start position:0%
electronic item tanks and electronic
 

00:02:17.470 --> 00:02:21.150 align:start position:0%
electronic item tanks and electronic
gates<00:02:18.660><c> most</c><00:02:19.660><c> businesses</c><00:02:20.200><c> simply</c><00:02:20.470><c> accept</c><00:02:21.010><c> that</c>

00:02:21.150 --> 00:02:21.160 align:start position:0%
gates most businesses simply accept that
 

00:02:21.160 --> 00:02:23.220 align:start position:0%
gates most businesses simply accept that
some<00:02:21.430><c> theft</c><00:02:21.670><c> is</c><00:02:21.850><c> going</c><00:02:22.060><c> to</c><00:02:22.150><c> take</c><00:02:22.330><c> place</c><00:02:22.510><c> and</c>

00:02:23.220 --> 00:02:23.230 align:start position:0%
some theft is going to take place and
 

00:02:23.230 --> 00:02:24.930 align:start position:0%
some theft is going to take place and
include<00:02:23.590><c> such</c><00:02:23.800><c> losses</c><00:02:24.250><c> in</c><00:02:24.430><c> their</c><00:02:24.550><c> business</c>

00:02:24.930 --> 00:02:24.940 align:start position:0%
include such losses in their business
 

00:02:24.940 --> 00:02:27.830 align:start position:0%
include such losses in their business
calculations<00:02:25.800><c> these</c><00:02:26.800><c> self-service</c><00:02:27.520><c> things</c>

00:02:27.830 --> 00:02:27.840 align:start position:0%
calculations these self-service things
 

00:02:27.840 --> 00:02:30.330 align:start position:0%
calculations these self-service things
saves<00:02:28.840><c> the</c><00:02:28.990><c> shop</c><00:02:29.200><c> quite</c><00:02:29.470><c> a</c><00:02:29.500><c> lot</c><00:02:29.680><c> of</c><00:02:29.709><c> money</c><00:02:29.920><c> it</c>

00:02:30.330 --> 00:02:30.340 align:start position:0%
saves the shop quite a lot of money it
 

00:02:30.340 --> 00:02:33.000 align:start position:0%
saves the shop quite a lot of money it
saves<00:02:30.700><c> them</c><00:02:30.910><c> on</c><00:02:31.030><c> library</c><00:02:31.390><c> costs</c><00:02:31.810><c> the</c><00:02:32.680><c> trouble</c>

00:02:33.000 --> 00:02:33.010 align:start position:0%
saves them on library costs the trouble
 

00:02:33.010 --> 00:02:35.010 align:start position:0%
saves them on library costs the trouble
is<00:02:33.160><c> it</c><00:02:33.760><c> also</c><00:02:34.030><c> makes</c><00:02:34.240><c> it</c><00:02:34.360><c> much</c><00:02:34.510><c> easier</c><00:02:34.780><c> for</c>

00:02:35.010 --> 00:02:35.020 align:start position:0%
is it also makes it much easier for
 

00:02:35.020 --> 00:02:38.310 align:start position:0%
is it also makes it much easier for
people<00:02:35.230><c> to</c><00:02:35.470><c> shoplift</c><00:02:36.660><c> so</c><00:02:37.660><c> why</c><00:02:37.840><c> do</c><00:02:37.900><c> they</c><00:02:38.110><c> have</c>

00:02:38.310 --> 00:02:38.320 align:start position:0%
people to shoplift so why do they have
 

00:02:38.320 --> 00:02:43.140 align:start position:0%
people to shoplift so why do they have
these<00:02:38.500><c> things</c><00:02:38.860><c> here</c><00:02:41.130><c> because</c><00:02:42.130><c> the</c><00:02:42.340><c> savings</c><00:02:42.940><c> on</c>

00:02:43.140 --> 00:02:43.150 align:start position:0%
these things here because the savings on
 

00:02:43.150 --> 00:02:45.449 align:start position:0%
these things here because the savings on
the<00:02:43.300><c> labor</c><00:02:43.510><c> costs</c><00:02:44.140><c> are</c><00:02:44.260><c> greater</c><00:02:44.680><c> than</c><00:02:45.130><c> the</c>

00:02:45.449 --> 00:02:45.459 align:start position:0%
the labor costs are greater than the
 

00:02:45.459 --> 00:02:47.270 align:start position:0%
the labor costs are greater than the
losses<00:02:45.820><c> on</c><00:02:45.970><c> the</c><00:02:46.060><c> shoplifting</c><00:02:46.660><c> shoplifting</c>

00:02:47.270 --> 00:02:47.280 align:start position:0%
losses on the shoplifting shoplifting
 

00:02:47.280 --> 00:02:49.770 align:start position:0%
losses on the shoplifting shoplifting
adds<00:02:48.280><c> to</c><00:02:48.520><c> the</c><00:02:48.610><c> cost</c><00:02:48.880><c> of</c><00:02:49.060><c> running</c><00:02:49.209><c> a</c><00:02:49.420><c> retail</c>

00:02:49.770 --> 00:02:49.780 align:start position:0%
adds to the cost of running a retail
 

00:02:49.780 --> 00:02:52.610 align:start position:0%
adds to the cost of running a retail
business<00:02:50.250><c> this</c><00:02:51.250><c> cost</c><00:02:51.550><c> is</c><00:02:51.730><c> estimated</c><00:02:52.360><c> at</c><00:02:52.480><c> about</c>

00:02:52.610 --> 00:02:52.620 align:start position:0%
business this cost is estimated at about
 

00:02:52.620 --> 00:02:55.350 align:start position:0%
business this cost is estimated at about
1/3<00:02:53.620><c> of</c><00:02:53.890><c> 1%</c><00:02:54.130><c> of</c><00:02:54.700><c> sales</c>

00:02:55.350 --> 00:02:55.360 align:start position:0%
1/3 of 1% of sales
 

00:02:55.360 --> 00:02:58.110 align:start position:0%
1/3 of 1% of sales
it<00:02:55.989><c> doesn't</c><00:02:56.350><c> sound</c><00:02:56.590><c> much</c><00:02:56.770><c> but</c><00:02:57.430><c> it</c><00:02:57.550><c> has</c><00:02:57.700><c> around</c>

00:02:58.110 --> 00:02:58.120 align:start position:0%
it doesn't sound much but it has around
 

00:02:58.120 --> 00:03:00.060 align:start position:0%
it doesn't sound much but it has around
a<00:02:58.239><c> hundred</c><00:02:58.390><c> of</c><00:02:58.690><c> thirty</c><00:02:58.900><c> pounds</c><00:02:59.560><c> to</c><00:03:00.040><c> the</c>

00:03:00.060 --> 00:03:00.070 align:start position:0%
a hundred of thirty pounds to the
 

00:03:00.070 --> 00:03:03.560 align:start position:0%
a hundred of thirty pounds to the
average<00:03:00.520><c> family's</c><00:03:01.000><c> annual</c><00:03:01.270><c> shopping</c><00:03:01.989><c> bill</c>

00:03:03.560 --> 00:03:03.570 align:start position:0%
average family's annual shopping bill
 

00:03:03.570 --> 00:03:06.960 align:start position:0%
average family's annual shopping bill
how<00:03:04.570><c> big</c><00:03:04.750><c> a</c><00:03:04.840><c> problem</c><00:03:05.170><c> is</c><00:03:05.890><c> shoplifting</c><00:03:06.580><c> for</c><00:03:06.880><c> the</c>

00:03:06.960 --> 00:03:06.970 align:start position:0%
how big a problem is shoplifting for the
 

00:03:06.970 --> 00:03:10.020 align:start position:0%
how big a problem is shoplifting for the
individual<00:03:07.510><c> store</c><00:03:07.870><c> it</c><00:03:08.860><c> varies</c><00:03:09.430><c> from</c><00:03:09.640><c> store</c><00:03:10.000><c> to</c>

00:03:10.020 --> 00:03:10.030 align:start position:0%
individual store it varies from store to
 

00:03:10.030 --> 00:03:14.759 align:start position:0%
individual store it varies from store to
store<00:03:10.680><c> it</c><00:03:11.680><c> varies</c><00:03:12.160><c> from</c><00:03:12.400><c> day</c><00:03:12.700><c> to</c><00:03:12.760><c> day</c><00:03:13.590><c> but</c><00:03:14.590><c> the</c>

00:03:14.759 --> 00:03:14.769 align:start position:0%
store it varies from day to day but the
 

00:03:14.769 --> 00:03:16.890 align:start position:0%
store it varies from day to day but the
pattern<00:03:15.250><c> conforms</c><00:03:16.209><c> to</c><00:03:16.299><c> a</c><00:03:16.420><c> normal</c>

00:03:16.890 --> 00:03:16.900 align:start position:0%
pattern conforms to a normal
 

00:03:16.900 --> 00:03:19.410 align:start position:0%
pattern conforms to a normal
distribution<00:03:17.670><c> and</c><00:03:18.670><c> that</c><00:03:18.850><c> means</c><00:03:19.060><c> that</c><00:03:19.269><c> we</c>

00:03:19.410 --> 00:03:19.420 align:start position:0%
distribution and that means that we
 

00:03:19.420 --> 00:03:22.860 align:start position:0%
distribution and that means that we
could<00:03:19.630><c> say</c><00:03:19.840><c> quite</c><00:03:20.260><c> a</c><00:03:20.290><c> lot</c><00:03:21.000><c> because</c><00:03:22.000><c> we</c><00:03:22.330><c> can</c><00:03:22.510><c> use</c>

00:03:22.860 --> 00:03:22.870 align:start position:0%
could say quite a lot because we can use
 

00:03:22.870 --> 00:03:25.199 align:start position:0%
could say quite a lot because we can use
our<00:03:23.110><c> normal</c><00:03:23.560><c> distribution</c><00:03:23.890><c> to</c><00:03:24.730><c> examine</c><00:03:25.150><c> a</c>

00:03:25.199 --> 00:03:25.209 align:start position:0%
our normal distribution to examine a
 

00:03:25.209 --> 00:03:27.810 align:start position:0%
our normal distribution to examine a
whole<00:03:25.450><c> range</c><00:03:25.810><c> of</c><00:03:26.080><c> problems</c><00:03:26.620><c> about</c><00:03:27.220><c> the</c><00:03:27.459><c> size</c>

00:03:27.810 --> 00:03:27.820 align:start position:0%
whole range of problems about the size
 

00:03:27.820 --> 00:03:30.810 align:start position:0%
whole range of problems about the size
of<00:03:28.120><c> the</c><00:03:28.239><c> loss</c><00:03:29.100><c> but</c><00:03:30.100><c> if</c><00:03:30.220><c> we're</c><00:03:30.340><c> going</c><00:03:30.489><c> to</c><00:03:30.610><c> do</c>

00:03:30.810 --> 00:03:30.820 align:start position:0%
of the loss but if we're going to do
 

00:03:30.820 --> 00:03:33.810 align:start position:0%
of the loss but if we're going to do
that<00:03:31.030><c> we</c><00:03:31.870><c> first</c><00:03:32.170><c> have</c><00:03:32.440><c> to</c><00:03:32.590><c> transform</c><00:03:33.459><c> the</c>

00:03:33.810 --> 00:03:33.820 align:start position:0%
that we first have to transform the
 

00:03:33.820 --> 00:03:36.570 align:start position:0%
that we first have to transform the
normal<00:03:34.390><c> distribution</c><00:03:35.049><c> into</c><00:03:35.560><c> the</c><00:03:35.890><c> standard</c>

00:03:36.570 --> 00:03:36.580 align:start position:0%
normal distribution into the standard
 

00:03:36.580 --> 00:03:39.600 align:start position:0%
normal distribution into the standard
normal<00:03:36.820><c> distribution</c><00:03:38.010><c> let's</c><00:03:39.010><c> see</c><00:03:39.190><c> how</c><00:03:39.310><c> we</c><00:03:39.370><c> do</c>

00:03:39.600 --> 00:03:39.610 align:start position:0%
normal distribution let's see how we do
 

00:03:39.610 --> 00:03:42.660 align:start position:0%
normal distribution let's see how we do
that<00:03:40.739><c> the</c><00:03:41.739><c> standard</c><00:03:42.190><c> normal</c><00:03:42.220><c> distribution</c>

00:03:42.660 --> 00:03:42.670 align:start position:0%
that the standard normal distribution
 

00:03:42.670 --> 00:03:45.539 align:start position:0%
that the standard normal distribution
has<00:03:43.329><c> a</c><00:03:43.360><c> mean</c><00:03:43.480><c> of</c><00:03:43.720><c> 0</c><00:03:44.170><c> and</c><00:03:44.260><c> a</c><00:03:45.100><c> standard</c><00:03:45.130><c> deviation</c>

00:03:45.539 --> 00:03:45.549 align:start position:0%
has a mean of 0 and a standard deviation
 

00:03:45.549 --> 00:03:48.870 align:start position:0%
has a mean of 0 and a standard deviation
equal<00:03:46.450><c> to</c><00:03:46.540><c> 1</c><00:03:46.780><c> we</c><00:03:47.590><c> can</c><00:03:47.709><c> look</c><00:03:48.040><c> at</c><00:03:48.190><c> the</c><00:03:48.280><c> area</c><00:03:48.700><c> under</c>

00:03:48.870 --> 00:03:48.880 align:start position:0%
equal to 1 we can look at the area under
 

00:03:48.880 --> 00:03:51.600 align:start position:0%
equal to 1 we can look at the area under
the<00:03:49.209><c> curve</c><00:03:49.239><c> by</c><00:03:50.170><c> converting</c><00:03:50.680><c> into</c><00:03:51.220><c> what</c><00:03:51.489><c> are</c>

00:03:51.600 --> 00:03:51.610 align:start position:0%
the curve by converting into what are
 

00:03:51.610 --> 00:03:55.259 align:start position:0%
the curve by converting into what are
called<00:03:51.870><c> z-scores</c><00:03:52.870><c> an</c><00:03:53.519><c> any</c><00:03:54.519><c> normal</c>

00:03:55.259 --> 00:03:55.269 align:start position:0%
called z-scores an any normal
 

00:03:55.269 --> 00:03:58.140 align:start position:0%
called z-scores an any normal
distribution<00:03:55.500><c> can</c><00:03:56.500><c> be</c><00:03:56.530><c> converted</c><00:03:57.060><c> using</c><00:03:58.060><c> the</c>

00:03:58.140 --> 00:03:58.150 align:start position:0%
distribution can be converted using the
 

00:03:58.150 --> 00:04:02.660 align:start position:0%
distribution can be converted using the
transformation<00:03:58.959><c> that</c><00:03:59.200><c> Z</c><00:04:00.100><c> equals</c><00:04:00.750><c> X</c><00:04:01.750><c> minus</c><00:04:01.989><c> mu</c>

00:04:02.660 --> 00:04:02.670 align:start position:0%
transformation that Z equals X minus mu
 

00:04:02.670 --> 00:04:05.980 align:start position:0%
transformation that Z equals X minus mu
divided<00:04:03.670><c> by</c><00:04:03.820><c> Sigma</c>

00:04:05.980 --> 00:04:05.990 align:start position:0%
 
 

00:04:05.990 --> 00:04:09.040 align:start position:0%
 
where<00:04:06.380><c> X</c><00:04:06.860><c> is</c><00:04:07.370><c> the</c><00:04:07.670><c> score</c><00:04:08.180><c> of</c><00:04:08.360><c> the</c><00:04:08.480><c> original</c>

00:04:09.040 --> 00:04:09.050 align:start position:0%
where X is the score of the original
 

00:04:09.050 --> 00:04:12.970 align:start position:0%
where X is the score of the original
normal<00:04:09.410><c> distribution</c><00:04:10.180><c> mu</c><00:04:11.180><c> is</c><00:04:11.480><c> the</c><00:04:12.110><c> mean</c><00:04:12.590><c> of</c>

00:04:12.970 --> 00:04:12.980 align:start position:0%
normal distribution mu is the mean of
 

00:04:12.980 --> 00:04:16.360 align:start position:0%
normal distribution mu is the mean of
the<00:04:13.160><c> original</c><00:04:13.670><c> normal</c><00:04:14.090><c> distribution</c><00:04:15.370><c> Sigma</c>

00:04:16.360 --> 00:04:16.370 align:start position:0%
the original normal distribution Sigma
 

00:04:16.370 --> 00:04:19.240 align:start position:0%
the original normal distribution Sigma
the<00:04:16.910><c> standard</c><00:04:17.360><c> deviation</c><00:04:17.989><c> of</c><00:04:18.200><c> the</c><00:04:18.770><c> original</c>

00:04:19.240 --> 00:04:19.250 align:start position:0%
the standard deviation of the original
 

00:04:19.250 --> 00:04:22.630 align:start position:0%
the standard deviation of the original
normal<00:04:19.640><c> distribution</c><00:04:20.270><c> and</c><00:04:20.739><c> Z</c><00:04:21.739><c> is</c><00:04:22.400><c> the</c>

00:04:22.630 --> 00:04:22.640 align:start position:0%
normal distribution and Z is the
 

00:04:22.640 --> 00:04:27.030 align:start position:0%
normal distribution and Z is the
standardized<00:04:23.240><c> variable</c><00:04:24.080><c> to</c><00:04:24.620><c> be</c><00:04:24.770><c> found</c>

00:04:27.030 --> 00:04:27.040 align:start position:0%
standardized variable to be found
 

00:04:27.040 --> 00:04:30.450 align:start position:0%
standardized variable to be found
be<00:04:27.730><c> aware</c><00:04:28.230><c> whilst</c><00:04:29.230><c> any</c><00:04:29.620><c> normal</c><00:04:30.280><c> distribution</c>

00:04:30.450 --> 00:04:30.460 align:start position:0%
be aware whilst any normal distribution
 

00:04:30.460 --> 00:04:33.450 align:start position:0%
be aware whilst any normal distribution
can<00:04:31.270><c> be</c><00:04:31.300><c> transformed</c><00:04:32.170><c> using</c><00:04:32.740><c> this</c><00:04:32.860><c> formula</c>

00:04:33.450 --> 00:04:33.460 align:start position:0%
can be transformed using this formula
 

00:04:33.460 --> 00:04:37.140 align:start position:0%
can be transformed using this formula
the<00:04:34.300><c> formula</c><00:04:34.510><c> will</c><00:04:35.170><c> not</c><00:04:35.680><c> convert</c><00:04:36.340><c> a</c><00:04:36.670><c> skewed</c>

00:04:37.140 --> 00:04:37.150 align:start position:0%
the formula will not convert a skewed
 

00:04:37.150 --> 00:04:41.000 align:start position:0%
the formula will not convert a skewed
distribution<00:04:37.590><c> into</c><00:04:38.590><c> one</c><00:04:38.800><c> that</c><00:04:38.950><c> is</c><00:04:39.010><c> not</c><00:04:39.430><c> skewed</c>

00:04:41.000 --> 00:04:41.010 align:start position:0%
distribution into one that is not skewed
 

00:04:41.010 --> 00:04:43.650 align:start position:0%
distribution into one that is not skewed
so<00:04:42.010><c> we're</c><00:04:42.160><c> looking</c><00:04:42.460><c> at</c><00:04:42.580><c> our</c><00:04:42.700><c> theft</c><00:04:43.150><c> problem</c>

00:04:43.650 --> 00:04:43.660 align:start position:0%
so we're looking at our theft problem
 

00:04:43.660 --> 00:04:46.920 align:start position:0%
so we're looking at our theft problem
because<00:04:44.650><c> the</c><00:04:44.860><c> theft</c><00:04:45.220><c> data</c><00:04:45.690><c> conforms</c><00:04:46.690><c> to</c><00:04:46.780><c> a</c>

00:04:46.920 --> 00:04:46.930 align:start position:0%
because the theft data conforms to a
 

00:04:46.930 --> 00:04:52.510 align:start position:0%
because the theft data conforms to a
normal<00:04:47.590><c> distribution</c>

00:04:52.510 --> 00:04:52.520 align:start position:0%
 
 

00:04:52.520 --> 00:04:55.390 align:start position:0%
 
as<00:04:52.699><c> the</c><00:04:52.819><c> storm</c><00:04:53.060><c> losses</c><00:04:53.509><c> on</c><00:04:54.050><c> average</c><00:04:54.590><c> about</c><00:04:54.860><c> 200</c>

00:04:55.390 --> 00:04:55.400 align:start position:0%
as the storm losses on average about 200
 

00:04:55.400 --> 00:04:58.360 align:start position:0%
as the storm losses on average about 200
pounds<00:04:55.729><c> a</c><00:04:55.849><c> day</c><00:04:56.440><c> and</c><00:04:57.440><c> we</c><00:04:57.560><c> know</c><00:04:57.650><c> the</c><00:04:57.860><c> standard</c>

00:04:58.360 --> 00:04:58.370 align:start position:0%
pounds a day and we know the standard
 

00:04:58.370 --> 00:05:02.550 align:start position:0%
pounds a day and we know the standard
deviation<00:04:59.060><c> of</c><00:04:59.180><c> the</c><00:04:59.360><c> daily</c><00:04:59.810><c> loss</c><00:04:59.990><c> is</c><00:05:00.620><c> 30</c><00:05:01.009><c> pounds</c>

00:05:02.550 --> 00:05:02.560 align:start position:0%
deviation of the daily loss is 30 pounds
 

00:05:02.560 --> 00:05:04.960 align:start position:0%
deviation of the daily loss is 30 pounds
now<00:05:03.560><c> let's</c><00:05:03.770><c> see</c><00:05:03.889><c> if</c><00:05:03.949><c> we</c><00:05:04.069><c> can</c><00:05:04.250><c> solve</c><00:05:04.490><c> a</c><00:05:04.789><c> number</c>

00:05:04.960 --> 00:05:04.970 align:start position:0%
now let's see if we can solve a number
 

00:05:04.970 --> 00:05:07.809 align:start position:0%
now let's see if we can solve a number
of<00:05:05.150><c> problems</c><00:05:05.270><c> for</c><00:05:05.960><c> the</c><00:05:06.050><c> store</c><00:05:06.259><c> owner</c><00:05:06.819><c> first</c>

00:05:07.809 --> 00:05:07.819 align:start position:0%
of problems for the store owner first
 

00:05:07.819 --> 00:05:10.420 align:start position:0%
of problems for the store owner first
what<00:05:08.569><c> are</c><00:05:08.660><c> the</c><00:05:08.750><c> chances</c><00:05:09.289><c> that</c><00:05:09.530><c> the</c><00:05:09.979><c> store</c><00:05:10.250><c> on</c>

00:05:10.420 --> 00:05:10.430 align:start position:0%
what are the chances that the store on
 

00:05:10.430 --> 00:05:13.180 align:start position:0%
what are the chances that the store on
any<00:05:10.550><c> given</c><00:05:10.880><c> day</c><00:05:11.000><c> will</c><00:05:11.479><c> lose</c><00:05:11.690><c> more</c><00:05:12.050><c> than</c><00:05:12.319><c> 250</c>

00:05:13.180 --> 00:05:13.190 align:start position:0%
any given day will lose more than 250
 

00:05:13.190 --> 00:05:18.760 align:start position:0%
any given day will lose more than 250
pounds<00:05:15.520><c> second</c><00:05:16.930><c> what</c><00:05:17.930><c> are</c><00:05:18.020><c> the</c><00:05:18.080><c> chances</c><00:05:18.710><c> that</c>

00:05:18.760 --> 00:05:18.770 align:start position:0%
pounds second what are the chances that
 

00:05:18.770 --> 00:05:23.710 align:start position:0%
pounds second what are the chances that
the<00:05:19.190><c> storm</c><00:05:19.520><c> will</c><00:05:19.729><c> lose</c><00:05:19.970><c> between</c><00:05:21.160><c> 250</c><00:05:22.160><c> and</c><00:05:22.720><c> 350</c>

00:05:23.710 --> 00:05:23.720 align:start position:0%
the storm will lose between 250 and 350
 

00:05:23.720 --> 00:05:25.800 align:start position:0%
the storm will lose between 250 and 350
pounds

00:05:25.800 --> 00:05:25.810 align:start position:0%
pounds
 

00:05:25.810 --> 00:05:30.730 align:start position:0%
pounds
third<00:05:27.550><c> what's</c><00:05:28.550><c> the</c><00:05:28.759><c> minimum</c><00:05:29.270><c> amount</c><00:05:29.590><c> that</c><00:05:30.590><c> the</c>

00:05:30.730 --> 00:05:30.740 align:start position:0%
third what's the minimum amount that the
 

00:05:30.740 --> 00:05:33.610 align:start position:0%
third what's the minimum amount that the
store<00:05:31.039><c> can</c><00:05:31.310><c> expect</c><00:05:31.759><c> to</c><00:05:31.940><c> lose</c><00:05:32.150><c> the</c><00:05:33.050><c> majority</c><00:05:33.590><c> of</c>

00:05:33.610 --> 00:05:33.620 align:start position:0%
store can expect to lose the majority of
 

00:05:33.620 --> 00:05:38.620 align:start position:0%
store can expect to lose the majority of
the<00:05:33.800><c> time</c><00:05:34.039><c> let's</c><00:05:34.490><c> say</c><00:05:35.199><c> 95%</c><00:05:36.199><c> of</c><00:05:36.319><c> the</c><00:05:36.440><c> days</c><00:05:37.630><c> we</c>

00:05:38.620 --> 00:05:38.630 align:start position:0%
the time let's say 95% of the days we
 

00:05:38.630 --> 00:05:42.040 align:start position:0%
the time let's say 95% of the days we
want<00:05:38.810><c> to</c><00:05:38.900><c> know</c><00:05:39.020><c> the</c><00:05:39.139><c> probability</c><00:05:39.470><c> P</c><00:05:40.400><c> that</c><00:05:41.330><c> X</c><00:05:41.569><c> is</c>

00:05:42.040 --> 00:05:42.050 align:start position:0%
want to know the probability P that X is
 

00:05:42.050 --> 00:05:45.879 align:start position:0%
want to know the probability P that X is
greater<00:05:42.470><c> than</c><00:05:42.740><c> 250</c><00:05:43.550><c> pounds</c><00:05:44.090><c> and</c><00:05:44.409><c> to</c><00:05:45.409><c> find</c><00:05:45.710><c> this</c>

00:05:45.879 --> 00:05:45.889 align:start position:0%
greater than 250 pounds and to find this
 

00:05:45.889 --> 00:05:48.100 align:start position:0%
greater than 250 pounds and to find this
we'll<00:05:46.130><c> have</c><00:05:46.400><c> to</c><00:05:46.580><c> transform</c><00:05:47.360><c> the</c><00:05:47.690><c> normal</c>

00:05:48.100 --> 00:05:48.110 align:start position:0%
we'll have to transform the normal
 

00:05:48.110 --> 00:05:51.730 align:start position:0%
we'll have to transform the normal
distribution<00:05:49.240><c> into</c><00:05:50.240><c> a</c><00:05:50.479><c> standardized</c><00:05:51.380><c> normal</c>

00:05:51.730 --> 00:05:51.740 align:start position:0%
distribution into a standardized normal
 

00:05:51.740 --> 00:05:56.020 align:start position:0%
distribution into a standardized normal
distribution<00:05:52.099><c> and</c><00:05:52.819><c> find</c><00:05:53.479><c> the</c><00:05:53.599><c> z-score</c><00:05:55.030><c> thus</c>

00:05:56.020 --> 00:05:56.030 align:start position:0%
distribution and find the z-score thus
 

00:05:56.030 --> 00:05:59.830 align:start position:0%
distribution and find the z-score thus
we<00:05:56.240><c> look</c><00:05:56.479><c> for</c><00:05:56.690><c> the</c><00:05:56.780><c> probability</c><00:05:57.259><c> P</c><00:05:57.919><c> of</c><00:05:58.340><c> Z</c><00:05:59.120><c> being</c>

00:05:59.830 --> 00:05:59.840 align:start position:0%
we look for the probability P of Z being
 

00:05:59.840 --> 00:06:04.790 align:start position:0%
we look for the probability P of Z being
greater<00:05:59.990><c> than</c><00:06:00.949><c> X</c><00:06:01.340><c> minus</c><00:06:01.639><c> mu</c><00:06:02.479><c> over</c><00:06:03.289><c> Sigma</c>

00:06:04.790 --> 00:06:04.800 align:start position:0%
greater than X minus mu over Sigma
 

00:06:04.800 --> 00:06:07.999 align:start position:0%
greater than X minus mu over Sigma
which<00:06:05.490><c> is</c><00:06:05.639><c> the</c><00:06:05.789><c> probability</c><00:06:06.030><c> that</c><00:06:06.750><c> Sid</c><00:06:07.560><c> is</c>

00:06:07.999 --> 00:06:08.009 align:start position:0%
which is the probability that Sid is
 

00:06:08.009 --> 00:06:13.879 align:start position:0%
which is the probability that Sid is
greater<00:06:08.759><c> than</c><00:06:09.530><c> 250</c><00:06:11.180><c> -</c><00:06:12.180><c> 200</c><00:06:12.840><c> the</c><00:06:13.020><c> average</c><00:06:13.590><c> store</c>

00:06:13.879 --> 00:06:13.889 align:start position:0%
greater than 250 - 200 the average store
 

00:06:13.889 --> 00:06:18.309 align:start position:0%
greater than 250 - 200 the average store
loss<00:06:14.300><c> over</c><00:06:15.300><c> 30</c><00:06:15.659><c> the</c><00:06:16.379><c> standard</c><00:06:16.770><c> deviation</c>

00:06:18.309 --> 00:06:18.319 align:start position:0%
loss over 30 the standard deviation
 

00:06:18.319 --> 00:06:21.800 align:start position:0%
loss over 30 the standard deviation
which<00:06:19.319><c> means</c><00:06:19.710><c> we</c><00:06:20.460><c> want</c><00:06:20.699><c> the</c><00:06:20.909><c> probability</c><00:06:21.300><c> that</c>

00:06:21.800 --> 00:06:21.810 align:start position:0%
which means we want the probability that
 

00:06:21.810 --> 00:06:26.990 align:start position:0%
which means we want the probability that
Z<00:06:22.409><c> is</c><00:06:22.680><c> greater</c><00:06:23.220><c> than</c><00:06:23.490><c> one</c><00:06:24.180><c> point</c><00:06:24.210><c> 6</c><00:06:24.780><c> 7</c><00:06:25.940><c> now</c><00:06:26.940><c> if</c>

00:06:26.990 --> 00:06:27.000 align:start position:0%
Z is greater than one point 6 7 now if
 

00:06:27.000 --> 00:06:29.300 align:start position:0%
Z is greater than one point 6 7 now if
we<00:06:27.120><c> look</c><00:06:27.300><c> up</c><00:06:27.449><c> one</c><00:06:27.990><c> point</c><00:06:28.319><c> six</c><00:06:28.650><c> seven</c><00:06:28.919><c> in</c><00:06:29.190><c> our</c>

00:06:29.300 --> 00:06:29.310 align:start position:0%
we look up one point six seven in our
 

00:06:29.310 --> 00:06:31.850 align:start position:0%
we look up one point six seven in our
standardized<00:06:30.060><c> normal</c><00:06:30.360><c> table</c><00:06:31.050><c> we</c><00:06:31.080><c> get</c><00:06:31.319><c> a</c><00:06:31.379><c> value</c>

00:06:31.850 --> 00:06:31.860 align:start position:0%
standardized normal table we get a value
 

00:06:31.860 --> 00:06:37.760 align:start position:0%
standardized normal table we get a value
of<00:06:31.940><c> naught</c><00:06:32.940><c> point</c><00:06:33.409><c> naught</c><00:06:34.580><c> 475</c><00:06:35.930><c> that</c><00:06:36.930><c> is</c><00:06:37.080><c> the</c>

00:06:37.760 --> 00:06:37.770 align:start position:0%
of naught point naught 475 that is the
 

00:06:37.770 --> 00:06:39.950 align:start position:0%
of naught point naught 475 that is the
answer<00:06:38.130><c> is</c><00:06:38.250><c> four</c><00:06:39.000><c> point</c><00:06:39.330><c> seven</c><00:06:39.599><c> five</c><00:06:39.900><c> percent</c>

00:06:39.950 --> 00:06:39.960 align:start position:0%
answer is four point seven five percent
 

00:06:39.960 --> 00:06:43.520 align:start position:0%
answer is four point seven five percent
of<00:06:40.470><c> the</c><00:06:40.560><c> time</c><00:06:40.800><c> on</c><00:06:41.310><c> any</c><00:06:41.699><c> given</c><00:06:41.970><c> day</c><00:06:42.349><c> there's</c><00:06:43.349><c> are</c>

00:06:43.520 --> 00:06:43.530 align:start position:0%
of the time on any given day there's are
 

00:06:43.530 --> 00:06:45.439 align:start position:0%
of the time on any given day there's are
just<00:06:43.770><c> less</c><00:06:43.979><c> than</c><00:06:44.009><c> five</c><00:06:44.400><c> percent</c><00:06:44.430><c> chance</c><00:06:45.060><c> that</c>

00:06:45.439 --> 00:06:45.449 align:start position:0%
just less than five percent chance that
 

00:06:45.449 --> 00:06:47.870 align:start position:0%
just less than five percent chance that
the<00:06:45.750><c> store</c><00:06:46.199><c> will</c><00:06:46.440><c> lose</c><00:06:46.680><c> more</c><00:06:47.069><c> than</c><00:06:47.400><c> two</c>

00:06:47.870 --> 00:06:47.880 align:start position:0%
the store will lose more than two
 

00:06:47.880 --> 00:06:51.800 align:start position:0%
the store will lose more than two
hundred<00:06:48.000><c> and</c><00:06:48.240><c> fifty</c><00:06:48.539><c> pounds</c>

00:06:51.800 --> 00:06:51.810 align:start position:0%
 
 

00:06:51.810 --> 00:06:53.690 align:start position:0%
 
now<00:06:52.440><c> let's</c><00:06:52.650><c> look</c><00:06:52.770><c> at</c><00:06:52.890><c> the</c><00:06:53.010><c> possibility</c><00:06:53.670><c> that</c>

00:06:53.690 --> 00:06:53.700 align:start position:0%
now let's look at the possibility that
 

00:06:53.700 --> 00:06:56.840 align:start position:0%
now let's look at the possibility that
the<00:06:54.060><c> loss</c><00:06:54.390><c> in</c><00:06:54.750><c> the</c><00:06:54.900><c> day</c><00:06:55.140><c> will</c><00:06:56.100><c> be</c><00:06:56.310><c> somewhere</c>

00:06:56.840 --> 00:06:56.850 align:start position:0%
the loss in the day will be somewhere
 

00:06:56.850 --> 00:07:01.520 align:start position:0%
the loss in the day will be somewhere
between<00:06:56.960><c> 250</c><00:06:57.960><c> and</c><00:06:58.230><c> 350</c><00:06:59.040><c> pounds</c><00:07:00.290><c> we'll</c><00:07:01.290><c> do</c><00:07:01.410><c> this</c>

00:07:01.520 --> 00:07:01.530 align:start position:0%
between 250 and 350 pounds we'll do this
 

00:07:01.530 --> 00:07:05.660 align:start position:0%
between 250 and 350 pounds we'll do this
in<00:07:01.710><c> three</c><00:07:01.950><c> steps</c><00:07:02.270><c> step</c><00:07:03.270><c> one</c><00:07:03.920><c> we</c><00:07:04.920><c> know</c><00:07:05.190><c> that</c><00:07:05.550><c> the</c>

00:07:05.660 --> 00:07:05.670 align:start position:0%
in three steps step one we know that the
 

00:07:05.670 --> 00:07:09.200 align:start position:0%
in three steps step one we know that the
probability<00:07:05.970><c> of</c><00:07:06.690><c> more</c><00:07:07.650><c> than</c><00:07:08.010><c> 250</c><00:07:08.730><c> pounds</c>

00:07:09.200 --> 00:07:09.210 align:start position:0%
probability of more than 250 pounds
 

00:07:09.210 --> 00:07:13.640 align:start position:0%
probability of more than 250 pounds
being<00:07:09.420><c> lost</c><00:07:09.720><c> is</c><00:07:10.020><c> naught</c><00:07:10.740><c> point</c><00:07:11.190><c> naught</c><00:07:11.930><c> 475</c><00:07:12.930><c> we</c>

00:07:13.640 --> 00:07:13.650 align:start position:0%
being lost is naught point naught 475 we
 

00:07:13.650 --> 00:07:16.190 align:start position:0%
being lost is naught point naught 475 we
just<00:07:13.980><c> did</c><00:07:14.250><c> that</c><00:07:14.490><c> in</c><00:07:14.760><c> the</c><00:07:15.210><c> first</c><00:07:15.420><c> problem</c><00:07:15.630><c> so</c>

00:07:16.190 --> 00:07:16.200 align:start position:0%
just did that in the first problem so
 

00:07:16.200 --> 00:07:19.130 align:start position:0%
just did that in the first problem so
the<00:07:16.320><c> probability</c><00:07:17.040><c> of</c><00:07:17.310><c> a</c><00:07:18.210><c> loss</c><00:07:18.510><c> of</c><00:07:18.690><c> less</c><00:07:19.110><c> than</c>

00:07:19.130 --> 00:07:19.140 align:start position:0%
the probability of a loss of less than
 

00:07:19.140 --> 00:07:23.870 align:start position:0%
the probability of a loss of less than
250<00:07:20.010><c> is</c><00:07:20.340><c> 1</c><00:07:21.300><c> minus</c><00:07:21.930><c> the</c><00:07:21.960><c> probability</c><00:07:22.290><c> that</c><00:07:23.250><c> X</c><00:07:23.520><c> is</c>

00:07:23.870 --> 00:07:23.880 align:start position:0%
250 is 1 minus the probability that X is
 

00:07:23.880 --> 00:07:27.290 align:start position:0%
250 is 1 minus the probability that X is
greater<00:07:24.090><c> than</c><00:07:24.360><c> 250</c><00:07:25.130><c> 1</c><00:07:26.130><c> minus</c><00:07:26.640><c> naught</c><00:07:27.030><c> point</c>

00:07:27.290 --> 00:07:27.300 align:start position:0%
greater than 250 1 minus naught point
 

00:07:27.300 --> 00:07:30.620 align:start position:0%
greater than 250 1 minus naught point
zero<00:07:27.660><c> four</c><00:07:27.990><c> seventy</c><00:07:28.440><c> five</c><00:07:28.700><c> equals</c><00:07:29.700><c> naught</c>

00:07:30.620 --> 00:07:30.630 align:start position:0%
zero four seventy five equals naught
 

00:07:30.630 --> 00:07:34.620 align:start position:0%
zero four seventy five equals naught
point<00:07:30.960><c> nine</c><00:07:31.500><c> five</c><00:07:31.800><c> two</c><00:07:32.160><c> five</c>

00:07:34.620 --> 00:07:34.630 align:start position:0%
 
 

00:07:34.630 --> 00:07:38.910 align:start position:0%
 
step<00:07:35.410><c> two</c><00:07:35.620><c> now</c><00:07:36.270><c> find</c><00:07:37.270><c> the</c><00:07:37.450><c> probability</c><00:07:38.230><c> of</c><00:07:38.500><c> the</c>

00:07:38.910 --> 00:07:38.920 align:start position:0%
step two now find the probability of the
 

00:07:38.920 --> 00:07:43.110 align:start position:0%
step two now find the probability of the
loss<00:07:39.130><c> being</c><00:07:39.400><c> more</c><00:07:39.880><c> than</c><00:07:40.240><c> 350</c><00:07:41.820><c> which</c><00:07:42.820><c> is</c><00:07:43.000><c> the</c>

00:07:43.110 --> 00:07:43.120 align:start position:0%
loss being more than 350 which is the
 

00:07:43.120 --> 00:07:47.750 align:start position:0%
loss being more than 350 which is the
probability<00:07:43.800><c> that</c><00:07:44.800><c> Z</c><00:07:45.220><c> is</c><00:07:45.520><c> greater</c><00:07:46.210><c> than</c><00:07:46.650><c> X</c>

00:07:47.750 --> 00:07:47.760 align:start position:0%
probability that Z is greater than X
 

00:07:47.760 --> 00:07:52.620 align:start position:0%
probability that Z is greater than X
minus<00:07:48.760><c> mu</c><00:07:49.060><c> over</c><00:07:49.570><c> Sigma</c><00:07:49.600><c> in</c><00:07:50.320><c> our</c><00:07:50.560><c> case</c><00:07:51.630><c> 350</c>

00:07:52.620 --> 00:07:52.630 align:start position:0%
minus mu over Sigma in our case 350
 

00:07:52.630 --> 00:07:56.730 align:start position:0%
minus mu over Sigma in our case 350
minus<00:07:53.410><c> 200</c><00:07:54.010><c> over</c><00:07:54.220><c> 30</c><00:07:55.500><c> which</c><00:07:56.500><c> is</c><00:07:56.530><c> the</c>

00:07:56.730 --> 00:07:56.740 align:start position:0%
minus 200 over 30 which is the
 

00:07:56.740 --> 00:08:00.230 align:start position:0%
minus 200 over 30 which is the
probability<00:07:57.130><c> that</c><00:07:57.580><c> said</c><00:07:57.880><c> is</c><00:07:58.060><c> greater</c><00:07:58.390><c> than</c><00:07:58.630><c> 5</c>

00:08:00.230 --> 00:08:00.240 align:start position:0%
probability that said is greater than 5
 

00:08:00.240 --> 00:08:02.940 align:start position:0%
probability that said is greater than 5
which<00:08:01.240><c> is</c><00:08:01.300><c> someone</c><00:08:01.840><c> likely</c><00:08:02.080><c> that</c>

00:08:02.940 --> 00:08:02.950 align:start position:0%
which is someone likely that
 

00:08:02.950 --> 00:08:09.240 align:start position:0%
which is someone likely that
approximates<00:08:03.760><c> to</c><00:08:03.880><c> 0</c><00:08:05.790><c> so</c><00:08:06.790><c> step</c><00:08:07.060><c> 3</c><00:08:08.250><c> the</c>

00:08:09.240 --> 00:08:09.250 align:start position:0%
approximates to 0 so step 3 the
 

00:08:09.250 --> 00:08:12.900 align:start position:0%
approximates to 0 so step 3 the
probability<00:08:09.720><c> that</c><00:08:10.720><c> X</c><00:08:10.990><c> will</c><00:08:11.290><c> lie</c><00:08:11.470><c> between</c><00:08:11.910><c> 250</c>

00:08:12.900 --> 00:08:12.910 align:start position:0%
probability that X will lie between 250
 

00:08:12.910 --> 00:08:14.940 align:start position:0%
probability that X will lie between 250
and<00:08:12.940><c> 350</c>

00:08:14.940 --> 00:08:14.950 align:start position:0%
and 350
 

00:08:14.950 --> 00:08:20.190 align:start position:0%
and 350
is<00:08:16.080><c> one</c><00:08:17.080><c> minus</c><00:08:17.830><c> the</c><00:08:18.760><c> probability</c><00:08:18.790><c> of</c><00:08:19.510><c> X</c><00:08:19.930><c> being</c>

00:08:20.190 --> 00:08:20.200 align:start position:0%
is one minus the probability of X being
 

00:08:20.200 --> 00:08:24.120 align:start position:0%
is one minus the probability of X being
less<00:08:20.350><c> than</c><00:08:20.830><c> 250</c><00:08:21.570><c> plus</c><00:08:22.570><c> the</c><00:08:22.800><c> probability</c><00:08:23.800><c> of</c><00:08:23.830><c> X</c>

00:08:24.120 --> 00:08:24.130 align:start position:0%
less than 250 plus the probability of X
 

00:08:24.130 --> 00:08:29.640 align:start position:0%
less than 250 plus the probability of X
being<00:08:24.460><c> more</c><00:08:25.240><c> than</c><00:08:25.450><c> 350</c><00:08:26.640><c> which</c><00:08:27.640><c> is</c><00:08:28.080><c> 1</c><00:08:29.080><c> minus</c>

00:08:29.640 --> 00:08:29.650 align:start position:0%
being more than 350 which is 1 minus
 

00:08:29.650 --> 00:08:34.640 align:start position:0%
being more than 350 which is 1 minus
naught<00:08:30.520><c> point</c><00:08:30.790><c> 5</c><00:08:31.120><c> 2</c><00:08:31.330><c> 5</c><00:08:31.650><c> plus</c><00:08:32.650><c> 0</c><00:08:33.300><c> which</c><00:08:34.300><c> equals</c>

00:08:34.640 --> 00:08:34.650 align:start position:0%
naught point 5 2 5 plus 0 which equals
 

00:08:34.650 --> 00:08:41.890 align:start position:0%
naught point 5 2 5 plus 0 which equals
naught<00:08:35.650><c> point</c><00:08:35.950><c> naught</c><00:08:36.540><c> 475</c>

00:08:41.890 --> 00:08:41.900 align:start position:0%
 
 

00:08:41.900 --> 00:08:43.870 align:start position:0%
 
in<00:08:42.440><c> this</c><00:08:42.560><c> last</c><00:08:42.800><c> problem</c><00:08:43.099><c> were</c><00:08:43.339><c> interested</c><00:08:43.789><c> in</c>

00:08:43.870 --> 00:08:43.880 align:start position:0%
in this last problem were interested in
 

00:08:43.880 --> 00:08:45.910 align:start position:0%
in this last problem were interested in
the<00:08:44.060><c> left</c><00:08:44.300><c> hand</c><00:08:44.630><c> tail</c><00:08:45.050><c> of</c><00:08:45.380><c> the</c><00:08:45.560><c> normal</c>

00:08:45.910 --> 00:08:45.920 align:start position:0%
the left hand tail of the normal
 

00:08:45.920 --> 00:08:50.620 align:start position:0%
the left hand tail of the normal
distribution<00:08:46.180><c> the</c><00:08:47.180><c> lowest</c><00:08:47.630><c> 5%</c><00:08:49.330><c> now</c><00:08:50.330><c> given</c>

00:08:50.620 --> 00:08:50.630 align:start position:0%
distribution the lowest 5% now given
 

00:08:50.630 --> 00:08:53.560 align:start position:0%
distribution the lowest 5% now given
that<00:08:50.750><c> a</c><00:08:50.839><c> lower</c><00:08:51.110><c> tail</c><00:08:51.529><c> value</c><00:08:52.100><c> of</c><00:08:52.270><c> minus</c><00:08:53.270><c> one</c>

00:08:53.560 --> 00:08:53.570 align:start position:0%
that a lower tail value of minus one
 

00:08:53.570 --> 00:08:56.829 align:start position:0%
that a lower tail value of minus one
point<00:08:53.870><c> six</c><00:08:54.290><c> five</c><00:08:54.560><c> gives</c><00:08:55.370><c> a</c><00:08:55.490><c> tail</c><00:08:55.730><c> area</c><00:08:56.270><c> of</c><00:08:56.510><c> five</c>

00:08:56.829 --> 00:08:56.839 align:start position:0%
point six five gives a tail area of five
 

00:08:56.839 --> 00:09:01.290 align:start position:0%
point six five gives a tail area of five
percent<00:08:57.380><c> we</c><00:08:58.130><c> have</c><00:08:58.810><c> minus</c><00:08:59.810><c> one</c><00:08:59.990><c> point</c><00:09:00.230><c> six</c><00:09:00.589><c> five</c>

00:09:01.290 --> 00:09:01.300 align:start position:0%
percent we have minus one point six five
 

00:09:01.300 --> 00:09:08.430 align:start position:0%
percent we have minus one point six five
equals<00:09:02.300><c> x</c><00:09:03.170><c> minus</c><00:09:04.100><c> 200</c><00:09:04.700><c> over</c><00:09:05.150><c> thirty</c><00:09:07.420><c> minus</c>

00:09:08.430 --> 00:09:08.440 align:start position:0%
equals x minus 200 over thirty minus
 

00:09:08.440 --> 00:09:12.370 align:start position:0%
equals x minus 200 over thirty minus
forty<00:09:09.440><c> nine</c><00:09:09.589><c> point</c><00:09:09.860><c> five</c><00:09:10.190><c> is</c><00:09:10.810><c> therefore</c><00:09:11.810><c> X</c>

00:09:12.370 --> 00:09:12.380 align:start position:0%
forty nine point five is therefore X
 

00:09:12.380 --> 00:09:14.870 align:start position:0%
forty nine point five is therefore X
minus<00:09:12.860><c> 200</c>

00:09:14.870 --> 00:09:14.880 align:start position:0%
minus 200
 

00:09:14.880 --> 00:09:19.280 align:start position:0%
minus 200
x<00:09:15.270><c> equals</c><00:09:15.690><c> a</c><00:09:16.680><c> hundred</c><00:09:17.640><c> and</c><00:09:17.730><c> fifty</c><00:09:18.120><c> point</c><00:09:19.020><c> five</c>

00:09:19.280 --> 00:09:19.290 align:start position:0%
x equals a hundred and fifty point five
 

00:09:19.290 --> 00:09:23.420 align:start position:0%
x equals a hundred and fifty point five
oh<00:09:20.360><c> so</c><00:09:21.360><c> the</c><00:09:21.510><c> store</c><00:09:21.750><c> can</c><00:09:22.020><c> expect</c><00:09:22.440><c> to</c><00:09:22.650><c> lose</c><00:09:22.860><c> at</c>

00:09:23.420 --> 00:09:23.430 align:start position:0%
oh so the store can expect to lose at
 

00:09:23.430 --> 00:09:25.700 align:start position:0%
oh so the store can expect to lose at
least<00:09:23.880><c> a</c><00:09:24.150><c> hundred</c><00:09:24.600><c> and</c><00:09:24.810><c> fifty</c><00:09:25.140><c> pounds</c><00:09:25.350><c> and</c>

00:09:25.700 --> 00:09:25.710 align:start position:0%
least a hundred and fifty pounds and
 

00:09:25.710 --> 00:09:32.540 align:start position:0%
least a hundred and fifty pounds and
fifty<00:09:26.010><c> pence</c><00:09:26.220><c> on</c><00:09:26.600><c> 95</c><00:09:27.600><c> percent</c><00:09:27.990><c> of</c><00:09:28.080><c> the</c><00:09:28.170><c> days</c><00:09:31.550><c> if</c>

00:09:32.540 --> 00:09:32.550 align:start position:0%
fifty pence on 95 percent of the days if
 

00:09:32.550 --> 00:09:34.340 align:start position:0%
fifty pence on 95 percent of the days if
we<00:09:32.730><c> know</c><00:09:32.850><c> the</c><00:09:33.000><c> data</c><00:09:33.150><c> conforms</c><00:09:33.750><c> to</c><00:09:33.840><c> a</c><00:09:33.960><c> normal</c>

00:09:34.340 --> 00:09:34.350 align:start position:0%
we know the data conforms to a normal
 

00:09:34.350 --> 00:09:36.560 align:start position:0%
we know the data conforms to a normal
distribution<00:09:34.670><c> and</c><00:09:35.670><c> we</c><00:09:35.730><c> know</c><00:09:35.970><c> the</c><00:09:36.090><c> mean</c><00:09:36.330><c> and</c>

00:09:36.560 --> 00:09:36.570 align:start position:0%
distribution and we know the mean and
 

00:09:36.570 --> 00:09:39.350 align:start position:0%
distribution and we know the mean and
the<00:09:37.290><c> standard</c><00:09:37.320><c> deviation</c><00:09:37.730><c> we</c><00:09:38.730><c> can</c><00:09:38.910><c> derive</c>

00:09:39.350 --> 00:09:39.360 align:start position:0%
the standard deviation we can derive
 

00:09:39.360 --> 00:09:41.300 align:start position:0%
the standard deviation we can derive
considerable<00:09:40.050><c> volumes</c><00:09:40.500><c> of</c><00:09:40.680><c> information</c>

00:09:41.300 --> 00:09:41.310 align:start position:0%
considerable volumes of information
 

00:09:41.310 --> 00:09:44.780 align:start position:0%
considerable volumes of information
about<00:09:41.490><c> losses</c><00:09:41.850><c> in</c><00:09:42.300><c> libraries</c><00:09:43.170><c> or</c><00:09:43.470><c> shops</c><00:09:44.070><c> or</c><00:09:44.550><c> a</c>

00:09:44.780 --> 00:09:44.790 align:start position:0%
about losses in libraries or shops or a
 

00:09:44.790 --> 00:09:49.030 align:start position:0%
about losses in libraries or shops or a
book<00:09:45.240><c> store</c><00:09:45.540><c> and</c><00:09:45.810><c> so</c><00:09:46.200><c> on</c><00:09:46.910><c> but</c><00:09:47.910><c> it's</c><00:09:48.060><c> not</c><00:09:48.390><c> just</c>

00:09:49.030 --> 00:09:49.040 align:start position:0%
book store and so on but it's not just
 

00:09:49.040 --> 00:09:52.790 align:start position:0%
book store and so on but it's not just
information<00:09:50.040><c> about</c><00:09:50.130><c> losses</c><00:09:50.840><c> we</c><00:09:51.840><c> can</c><00:09:52.050><c> also</c><00:09:52.230><c> see</c>

00:09:52.790 --> 00:09:52.800 align:start position:0%
information about losses we can also see
 

00:09:52.800 --> 00:09:56.150 align:start position:0%
information about losses we can also see
many<00:09:53.700><c> other</c><00:09:53.850><c> things</c><00:09:54.350><c> the</c><00:09:55.350><c> distribution</c><00:09:56.040><c> of</c>

00:09:56.150 --> 00:09:56.160 align:start position:0%
many other things the distribution of
 

00:09:56.160 --> 00:09:59.030 align:start position:0%
many other things the distribution of
wealth<00:09:56.400><c> and</c><00:09:56.670><c> income</c><00:09:57.200><c> the</c><00:09:58.200><c> probability</c><00:09:59.010><c> of</c>

00:09:59.030 --> 00:09:59.040 align:start position:0%
wealth and income the probability of
 

00:09:59.040 --> 00:10:01.790 align:start position:0%
wealth and income the probability of
returns<00:09:59.610><c> for</c><00:10:00.480><c> some</c><00:10:00.690><c> investment</c><00:10:01.290><c> in</c><00:10:01.380><c> the</c><00:10:01.530><c> stock</c>

00:10:01.790 --> 00:10:01.800 align:start position:0%
returns for some investment in the stock
 

00:10:01.800 --> 00:10:04.430 align:start position:0%
returns for some investment in the stock
market<00:10:02.340><c> the</c><00:10:03.210><c> amount</c><00:10:03.300><c> of</c><00:10:03.630><c> intelligence</c><00:10:04.350><c> that</c>

00:10:04.430 --> 00:10:04.440 align:start position:0%
market the amount of intelligence that
 

00:10:04.440 --> 00:10:08.810 align:start position:0%
market the amount of intelligence that
people<00:10:04.890><c> have</c><00:10:05.070><c> the</c><00:10:05.520><c> list</c><00:10:05.790><c> is</c><00:10:06.060><c> endless</c><00:10:07.820><c> the</c>

00:10:08.810 --> 00:10:08.820 align:start position:0%
people have the list is endless the
 

00:10:08.820 --> 00:10:11.300 align:start position:0%
people have the list is endless the
normal<00:10:09.330><c> distribution</c><00:10:09.510><c> then</c><00:10:10.110><c> is</c><00:10:10.350><c> one</c><00:10:11.070><c> of</c><00:10:11.190><c> the</c>

00:10:11.300 --> 00:10:11.310 align:start position:0%
normal distribution then is one of the
 

00:10:11.310 --> 00:10:29.390 align:start position:0%
normal distribution then is one of the
most<00:10:11.550><c> important</c><00:10:12.210><c> concepts</c><00:10:12.810><c> its</c><00:10:13.380><c> statistics</c>

00:10:29.390 --> 00:10:29.400 align:start position:0%
 
 

00:10:29.400 --> 00:10:31.460 align:start position:0%
 
you