[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.61,0:00:04.10,Default,,0000,0000,0000,,Let's do another problem from\Nthe normal distribution
Dialogue: 0,0:00:04.10,0:00:10.12,Default,,0000,0000,0000,,section of ck12.org's\NAP statistics book.
Dialogue: 0,0:00:10.12,0:00:11.77,Default,,0000,0000,0000,,And I'm using theirs because\Nit's Open Source and it's
Dialogue: 0,0:00:11.77,0:00:13.99,Default,,0000,0000,0000,,actually quite a good book.
Dialogue: 0,0:00:13.99,0:00:16.48,Default,,0000,0000,0000,,The problems are, I think,\Ngood practice for us.
Dialogue: 0,0:00:16.48,0:00:19.07,Default,,0000,0000,0000,,So let's see, number 3.
Dialogue: 0,0:00:19.07,0:00:20.39,Default,,0000,0000,0000,,You could go to their\Nsite and I think you
Dialogue: 0,0:00:20.39,0:00:21.69,Default,,0000,0000,0000,,can download the book.
Dialogue: 0,0:00:21.69,0:00:26.18,Default,,0000,0000,0000,,Assume that the mean eight of 1\Nyear old girls in the U.S. is a
Dialogue: 0,0:00:26.18,0:00:28.92,Default,,0000,0000,0000,,normally distributed-- or is\Nnormally distributed with the
Dialogue: 0,0:00:28.92,0:00:32.33,Default,,0000,0000,0000,,mean of about 9.5 grams.
Dialogue: 0,0:00:32.33,0:00:33.82,Default,,0000,0000,0000,,That's got to be kilograms.
Dialogue: 0,0:00:33.82,0:00:35.93,Default,,0000,0000,0000,,I have a 10 month old son\Nand he weighs about 20
Dialogue: 0,0:00:35.93,0:00:39.57,Default,,0000,0000,0000,,pounds which is about 9\Nkilograms not 9.5 grams.
Dialogue: 0,0:00:39.57,0:00:41.04,Default,,0000,0000,0000,,9.5 grams is nothing.
Dialogue: 0,0:00:41.04,0:00:43.90,Default,,0000,0000,0000,,This would be talking about\Nlike mice or something.
Dialogue: 0,0:00:43.90,0:00:44.94,Default,,0000,0000,0000,,This has got to be kilograms.
Dialogue: 0,0:00:44.94,0:00:47.35,Default,,0000,0000,0000,,But anyway, it's about\N9.5 kilograms with a
Dialogue: 0,0:00:47.35,0:00:51.05,Default,,0000,0000,0000,,standard deviation of\Napproximately 1.1 grams.
Dialogue: 0,0:00:51.05,0:00:56.40,Default,,0000,0000,0000,,So the mean is equal to 9.5\Nkilograms I'm assuming and
Dialogue: 0,0:00:56.40,0:01:01.13,Default,,0000,0000,0000,,the standard deviation\Nis equal to 1.1 grams.
Dialogue: 0,0:01:01.13,0:01:04.84,Default,,0000,0000,0000,,Without using a calculator-- so\Nthat's an interesting clue--
Dialogue: 0,0:01:04.84,0:01:08.95,Default,,0000,0000,0000,,estimate the percentage of 1\Nyear old girls in the U.S. that
Dialogue: 0,0:01:08.95,0:01:09.100,Default,,0000,0000,0000,,meet the following conditions.
Dialogue: 0,0:01:09.100,0:01:12.91,Default,,0000,0000,0000,,So when they say that without a\Ncalculator estimate that's a
Dialogue: 0,0:01:12.91,0:01:15.25,Default,,0000,0000,0000,,big clue or a big giveaway that\Nwe're supposed to use
Dialogue: 0,0:01:15.25,0:01:16.35,Default,,0000,0000,0000,,the empirical rule.
Dialogue: 0,0:01:20.04,0:01:27.48,Default,,0000,0000,0000,,Empirical rule sometimes\Ncalled the 68-95-99.7 rule.
Dialogue: 0,0:01:27.48,0:01:29.96,Default,,0000,0000,0000,,And if you remember this\Nis the name of the rule
Dialogue: 0,0:01:29.96,0:01:31.50,Default,,0000,0000,0000,,you've essentially\Nremembered the rule.
Dialogue: 0,0:01:31.50,0:01:33.52,Default,,0000,0000,0000,,What that tells us that if we\Nhave a normal distribution--
Dialogue: 0,0:01:33.52,0:01:35.80,Default,,0000,0000,0000,,I'll do a bit of a review\Nhere before we jump
Dialogue: 0,0:01:35.80,0:01:36.75,Default,,0000,0000,0000,,into this problem.
Dialogue: 0,0:01:36.75,0:01:38.75,Default,,0000,0000,0000,,If we have a normal\Ndistribution-- let me draw
Dialogue: 0,0:01:38.75,0:01:40.48,Default,,0000,0000,0000,,a normal distribution.
Dialogue: 0,0:01:40.48,0:01:42.90,Default,,0000,0000,0000,,It looks like that.
Dialogue: 0,0:01:42.90,0:01:44.24,Default,,0000,0000,0000,,That's my normal distribution.
Dialogue: 0,0:01:44.24,0:01:45.94,Default,,0000,0000,0000,,I didn't draw it perfectly\Nbut you get the idea.
Dialogue: 0,0:01:45.94,0:01:47.56,Default,,0000,0000,0000,,It should be symmetrical.
Dialogue: 0,0:01:47.56,0:01:49.98,Default,,0000,0000,0000,,This is our mean right there.
Dialogue: 0,0:01:49.98,0:01:50.84,Default,,0000,0000,0000,,That's our mean.
Dialogue: 0,0:01:50.84,0:01:54.81,Default,,0000,0000,0000,,If we go one standard deviation\Nabove the mean and one standard
Dialogue: 0,0:01:54.81,0:02:00.35,Default,,0000,0000,0000,,deviation below the mean,\Nso this is our mean plus
Dialogue: 0,0:02:00.35,0:02:01.78,Default,,0000,0000,0000,,one standard deviation.
Dialogue: 0,0:02:01.78,0:02:05.73,Default,,0000,0000,0000,,This is our mean minus\None standard deviation.
Dialogue: 0,0:02:05.73,0:02:08.71,Default,,0000,0000,0000,,The probability of finding a\Nresult if we're dealing with a
Dialogue: 0,0:02:08.71,0:02:12.08,Default,,0000,0000,0000,,perfect normal distribution\Nthat's between one standard
Dialogue: 0,0:02:12.08,0:02:14.64,Default,,0000,0000,0000,,deviation below the mean and\None standard deviation above
Dialogue: 0,0:02:14.64,0:02:19.32,Default,,0000,0000,0000,,the mean-- that would be this\Narea-- and it would be,
Dialogue: 0,0:02:19.32,0:02:23.04,Default,,0000,0000,0000,,you could guess, 68%.
Dialogue: 0,0:02:23.04,0:02:26.43,Default,,0000,0000,0000,,68% chance you're going to get\Nsomething within one standard
Dialogue: 0,0:02:26.43,0:02:27.75,Default,,0000,0000,0000,,deviation of the mean.
Dialogue: 0,0:02:27.75,0:02:30.14,Default,,0000,0000,0000,,Either a standard deviation\Nbelow or above or
Dialogue: 0,0:02:30.14,0:02:31.45,Default,,0000,0000,0000,,anywhere in between.
Dialogue: 0,0:02:31.45,0:02:34.50,Default,,0000,0000,0000,,Now, if we're talking about two\Nstandard deviations around the
Dialogue: 0,0:02:34.50,0:02:37.17,Default,,0000,0000,0000,,mean-- so if we go down another\Nstandard deviation, we go down
Dialogue: 0,0:02:37.17,0:02:39.57,Default,,0000,0000,0000,,another standard deviation in\Nthat direction and another
Dialogue: 0,0:02:39.57,0:02:41.78,Default,,0000,0000,0000,,standard deviation above the\Nmean-- and we were to ask
Dialogue: 0,0:02:41.78,0:02:43.19,Default,,0000,0000,0000,,ourselves what's the\Nprobability of finding
Dialogue: 0,0:02:43.19,0:02:47.36,Default,,0000,0000,0000,,something within those two or\Nwithin that range, then it's,
Dialogue: 0,0:02:47.36,0:02:50.74,Default,,0000,0000,0000,,you could guess it, 95%.
Dialogue: 0,0:02:50.74,0:02:53.06,Default,,0000,0000,0000,,And that includes this\Nmiddle area right here.
Dialogue: 0,0:02:53.06,0:02:56.51,Default,,0000,0000,0000,,So the 68% is a\Nsubset of that 95%.
Dialogue: 0,0:02:56.51,0:02:58.14,Default,,0000,0000,0000,,And I think you know\Nwhere this is going.
Dialogue: 0,0:02:58.14,0:03:01.36,Default,,0000,0000,0000,,If we go three standard\Ndeviations below the mean and
Dialogue: 0,0:03:01.36,0:03:06.82,Default,,0000,0000,0000,,above the mean, the empirical\Nrule or the 68-95-99.7 rule
Dialogue: 0,0:03:06.82,0:03:15.74,Default,,0000,0000,0000,,tells us that there is a 99.7%\Nchance of finding a result in a
Dialogue: 0,0:03:15.74,0:03:19.12,Default,,0000,0000,0000,,normal distribution that is\Nwithin three standard
Dialogue: 0,0:03:19.12,0:03:20.11,Default,,0000,0000,0000,,deviations of the mean.
Dialogue: 0,0:03:20.11,0:03:23.23,Default,,0000,0000,0000,,So above three standard\Ndeviations below the mean
Dialogue: 0,0:03:23.23,0:03:26.03,Default,,0000,0000,0000,,and below three standard\Ndeviation above the mean.
Dialogue: 0,0:03:26.03,0:03:27.87,Default,,0000,0000,0000,,That's what the empirical\Nrule tells us.
Dialogue: 0,0:03:27.87,0:03:30.96,Default,,0000,0000,0000,,Now let's see if we can\Napply it to this problem.
Dialogue: 0,0:03:30.96,0:03:33.14,Default,,0000,0000,0000,,So they gave us the mean and\Nthe standard deviation.
Dialogue: 0,0:03:33.14,0:03:34.55,Default,,0000,0000,0000,,Let me draw that out.
Dialogue: 0,0:03:34.55,0:03:38.55,Default,,0000,0000,0000,,Let me draw my axis\Nfirst as best as I can.
Dialogue: 0,0:03:38.55,0:03:39.60,Default,,0000,0000,0000,,That's my axis.
Dialogue: 0,0:03:39.60,0:03:41.41,Default,,0000,0000,0000,,Let me draw my bell curve.
Dialogue: 0,0:03:45.92,0:03:49.09,Default,,0000,0000,0000,,That's about as good as a\Nbell curve as you can expect
Dialogue: 0,0:03:49.09,0:03:50.92,Default,,0000,0000,0000,,a freehand drawer to do.
Dialogue: 0,0:03:50.92,0:03:54.14,Default,,0000,0000,0000,,And the mean here is 9.-- and\Nthis should be symmetric.
Dialogue: 0,0:03:54.14,0:03:55.71,Default,,0000,0000,0000,,This height should be the\Nsame as that height there.
Dialogue: 0,0:03:55.71,0:03:57.60,Default,,0000,0000,0000,,I think you get the idea.
Dialogue: 0,0:03:57.60,0:03:59.26,Default,,0000,0000,0000,,I'm not a computer.
Dialogue: 0,0:03:59.26,0:04:02.39,Default,,0000,0000,0000,,9.5 is the mean.
Dialogue: 0,0:04:02.39,0:04:03.37,Default,,0000,0000,0000,,I won't write the units.
Dialogue: 0,0:04:03.37,0:04:04.58,Default,,0000,0000,0000,,It's all in kilograms.
Dialogue: 0,0:04:04.58,0:04:11.33,Default,,0000,0000,0000,,One standard deviation above\Nthe mean we should add 1.1 to
Dialogue: 0,0:04:11.33,0:04:14.22,Default,,0000,0000,0000,,that because they told us the\Nstandard deviation is 1.1.
Dialogue: 0,0:04:14.22,0:04:16.82,Default,,0000,0000,0000,,That's going to be 10.6.
Dialogue: 0,0:04:16.82,0:04:19.62,Default,,0000,0000,0000,,If we go-- let me just draw a\Nlittle dotted line there-- 1
Dialogue: 0,0:04:19.62,0:04:25.99,Default,,0000,0000,0000,,standard deviation below the\Nmean we're going it subtract
Dialogue: 0,0:04:25.99,0:04:34.11,Default,,0000,0000,0000,,1.1 from 9.5 and so\Nthat would be 8.4.
Dialogue: 0,0:04:34.11,0:04:37.62,Default,,0000,0000,0000,,If we go two standard\Ndeviations above the mean
Dialogue: 0,0:04:37.62,0:04:40.40,Default,,0000,0000,0000,,we would add another\Nstandard deviation here.
Dialogue: 0,0:04:40.40,0:04:40.61,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:04:40.61,0:04:41.89,Default,,0000,0000,0000,,We went one standard\Ndeviations, two
Dialogue: 0,0:04:41.89,0:04:42.70,Default,,0000,0000,0000,,standard deviations.
Dialogue: 0,0:04:42.70,0:04:44.44,Default,,0000,0000,0000,,That would get us to 11.7.
Dialogue: 0,0:04:44.44,0:04:47.04,Default,,0000,0000,0000,,And if we were to go three\Nstandard deviations
Dialogue: 0,0:04:47.04,0:04:48.91,Default,,0000,0000,0000,,we'd add 1.1 again.
Dialogue: 0,0:04:48.91,0:04:50.72,Default,,0000,0000,0000,,That would get us to 12.8.
Dialogue: 0,0:04:50.72,0:04:53.82,Default,,0000,0000,0000,,Doing it on the other side,\None standard deviation
Dialogue: 0,0:04:53.82,0:04:55.38,Default,,0000,0000,0000,,below the mean is 8.4.
Dialogue: 0,0:04:55.38,0:04:58.48,Default,,0000,0000,0000,,Two standard deviations below\Nthe mean-- subtract 1.1
Dialogue: 0,0:04:58.48,0:05:00.91,Default,,0000,0000,0000,,again-- would be 7.3.
Dialogue: 0,0:05:00.91,0:05:03.38,Default,,0000,0000,0000,,And then three standard\Ndeviations below the mean--
Dialogue: 0,0:05:03.38,0:05:07.28,Default,,0000,0000,0000,,which we'd write there--\Nwould be 6.2 kilograms.
Dialogue: 0,0:05:07.28,0:05:08.86,Default,,0000,0000,0000,,So that's our set up\Nfor the problem.
Dialogue: 0,0:05:08.86,0:05:12.07,Default,,0000,0000,0000,,So what's the probability that\Nwe would find a one year old
Dialogue: 0,0:05:12.07,0:05:17.73,Default,,0000,0000,0000,,girl in the U.S. that weighs\Nless than 8.4 kilograms.
Dialogue: 0,0:05:17.73,0:05:19.33,Default,,0000,0000,0000,,Or maybe I should say\Nwhose mass is less
Dialogue: 0,0:05:19.33,0:05:21.64,Default,,0000,0000,0000,,than 8.4 kilograms.
Dialogue: 0,0:05:21.64,0:05:25.15,Default,,0000,0000,0000,,So if we look here, the\Nprobability of finding a baby
Dialogue: 0,0:05:25.15,0:05:28.07,Default,,0000,0000,0000,,or a female baby who is one\Nyear old with a mass or a
Dialogue: 0,0:05:28.07,0:05:30.92,Default,,0000,0000,0000,,weight of less than 8.4\Nkilograms, that's this
Dialogue: 0,0:05:30.92,0:05:31.61,Default,,0000,0000,0000,,area right here.
Dialogue: 0,0:05:31.61,0:05:35.07,Default,,0000,0000,0000,,I said mass because kilograms\Nis actually a unit of mass.
Dialogue: 0,0:05:35.07,0:05:36.94,Default,,0000,0000,0000,,Most people use it\Nas weight as well.
Dialogue: 0,0:05:36.94,0:05:38.47,Default,,0000,0000,0000,,So that's that\Narea right there.
Dialogue: 0,0:05:38.47,0:05:40.95,Default,,0000,0000,0000,,So how can we figure out\Nthat area under this
Dialogue: 0,0:05:40.95,0:05:43.90,Default,,0000,0000,0000,,normal distribution using\Nthe empirical rule?
Dialogue: 0,0:05:43.90,0:05:47.28,Default,,0000,0000,0000,,Well, we know what\Nthis area is.
Dialogue: 0,0:05:47.28,0:05:52.37,Default,,0000,0000,0000,,We know what this area between\Nminus one standard deviation
Dialogue: 0,0:05:52.37,0:05:54.50,Default,,0000,0000,0000,,and plus one standard\Ndeviation is.
Dialogue: 0,0:05:54.50,0:05:55.92,Default,,0000,0000,0000,,We know that is 68%.
Dialogue: 0,0:05:58.43,0:06:01.72,Default,,0000,0000,0000,,And if that's 68% then that\Nmeans in the parts that
Dialogue: 0,0:06:01.72,0:06:04.36,Default,,0000,0000,0000,,aren't in that middle\Nregion you have 32%.
Dialogue: 0,0:06:04.36,0:06:07.20,Default,,0000,0000,0000,,Because the area under the\Nentire normal distribution is
Dialogue: 0,0:06:07.20,0:06:11.38,Default,,0000,0000,0000,,100 or 100% or 1, depending on\Nhow you want to think about it.
Dialogue: 0,0:06:11.38,0:06:14.49,Default,,0000,0000,0000,,Because you can't have-- well,\Nall of the possibilities
Dialogue: 0,0:06:14.49,0:06:17.88,Default,,0000,0000,0000,,combined can only add up to 1.
Dialogue: 0,0:06:17.88,0:06:21.48,Default,,0000,0000,0000,,You can't have it more\Nthan 100% there.
Dialogue: 0,0:06:21.48,0:06:27.27,Default,,0000,0000,0000,,So if you add up this leg and\Nthis leg-- so this plus that
Dialogue: 0,0:06:27.27,0:06:29.49,Default,,0000,0000,0000,,leg is going to be\Nthe remainder.
Dialogue: 0,0:06:29.49,0:06:32.59,Default,,0000,0000,0000,,So 100 minus 68, that's 32.
Dialogue: 0,0:06:32.59,0:06:33.92,Default,,0000,0000,0000,,32%.
Dialogue: 0,0:06:33.92,0:06:37.82,Default,,0000,0000,0000,,32% is if you add up\Nthis left leg and this
Dialogue: 0,0:06:37.82,0:06:39.24,Default,,0000,0000,0000,,right leg over here.
Dialogue: 0,0:06:39.24,0:06:41.12,Default,,0000,0000,0000,,And this is a perfect\Nnormal distribution.
Dialogue: 0,0:06:41.12,0:06:42.54,Default,,0000,0000,0000,,They told us it's\Nnormally distributed.
Dialogue: 0,0:06:42.54,0:06:44.78,Default,,0000,0000,0000,,So it's going to be\Nperfectly symmetrical.
Dialogue: 0,0:06:44.78,0:06:48.73,Default,,0000,0000,0000,,So if this side and that side\Nadd up to 32 but they're both
Dialogue: 0,0:06:48.73,0:06:51.82,Default,,0000,0000,0000,,symmetrical, meaning they have\Nthe exact same area, then this
Dialogue: 0,0:06:51.82,0:06:56.49,Default,,0000,0000,0000,,side right here-- I'll do it in\Npink-- this side right here--
Dialogue: 0,0:06:56.49,0:07:00.02,Default,,0000,0000,0000,,it ended up looking more\Nlike purple-- would be 16%.
Dialogue: 0,0:07:00.02,0:07:02.70,Default,,0000,0000,0000,,And this side right\Nhere would be 16%.
Dialogue: 0,0:07:02.70,0:07:05.90,Default,,0000,0000,0000,,So your probability of getting\Na result more than one standard
Dialogue: 0,0:07:05.90,0:07:08.28,Default,,0000,0000,0000,,deviation above the mean-- so\Nthat's this right hand
Dialogue: 0,0:07:08.28,0:07:09.76,Default,,0000,0000,0000,,side, would be 16%.
Dialogue: 0,0:07:09.76,0:07:13.04,Default,,0000,0000,0000,,Or the probability of having a\Nresult less than one standard
Dialogue: 0,0:07:13.04,0:07:17.05,Default,,0000,0000,0000,,deviation below that mean,\Nthat's this right here, 16%.
Dialogue: 0,0:07:17.05,0:07:19.06,Default,,0000,0000,0000,,So they want to know the\Nprobability of having a
Dialogue: 0,0:07:19.06,0:07:23.14,Default,,0000,0000,0000,,baby at one years old\Nless than 8.4 kilograms.
Dialogue: 0,0:07:23.14,0:07:27.97,Default,,0000,0000,0000,,Less than 8.4 kilograms\Nis this area right here.
Dialogue: 0,0:07:27.97,0:07:29.50,Default,,0000,0000,0000,,And that's 16%.
Dialogue: 0,0:07:29.50,0:07:33.27,Default,,0000,0000,0000,,So that's 16% for part a.
Dialogue: 0,0:07:33.27,0:07:38.28,Default,,0000,0000,0000,,Let's do part b: between 7.3\Nand 11.7 point seven kilograms.
Dialogue: 0,0:07:38.28,0:07:41.13,Default,,0000,0000,0000,,So between 7.3--\Nthat's right there.
Dialogue: 0,0:07:41.13,0:07:47.12,Default,,0000,0000,0000,,That's two standard deviations\Nbelow the mean-- and 11.7, one,
Dialogue: 0,0:07:47.12,0:07:49.10,Default,,0000,0000,0000,,two standard deviations\Nabove the mean.
Dialogue: 0,0:07:49.10,0:07:51.26,Default,,0000,0000,0000,,So there's essentially asking\Nus what's the probability of
Dialogue: 0,0:07:51.26,0:07:54.34,Default,,0000,0000,0000,,getting a result within two\Nstandard deviations
Dialogue: 0,0:07:54.34,0:07:55.23,Default,,0000,0000,0000,,of the mean, right?
Dialogue: 0,0:07:55.23,0:07:57.04,Default,,0000,0000,0000,,This is the mean right here.
Dialogue: 0,0:07:57.04,0:08:00.25,Default,,0000,0000,0000,,This is two standard\Ndeviations below.
Dialogue: 0,0:08:00.25,0:08:02.63,Default,,0000,0000,0000,,This is two standard\Ndeviations above.
Dialogue: 0,0:08:02.63,0:08:04.13,Default,,0000,0000,0000,,Well that's pretty\Nstraightforward.
Dialogue: 0,0:08:04.13,0:08:07.49,Default,,0000,0000,0000,,The empirical rule tells us\Nbetween two standard deviations
Dialogue: 0,0:08:07.49,0:08:13.95,Default,,0000,0000,0000,,you have a 95% chance of\Ngetting a result that is within
Dialogue: 0,0:08:13.95,0:08:15.14,Default,,0000,0000,0000,,two standard deviations.
Dialogue: 0,0:08:15.14,0:08:17.74,Default,,0000,0000,0000,,So the empirical rule just\Ngives us that answer.
Dialogue: 0,0:08:17.74,0:08:21.44,Default,,0000,0000,0000,,And then finally, part c: the\Nprobability of having a one
Dialogue: 0,0:08:21.44,0:08:25.51,Default,,0000,0000,0000,,year old U.S. a baby girl\Nmore than 12.8 kilograms.
Dialogue: 0,0:08:25.51,0:08:28.31,Default,,0000,0000,0000,,So 12.8 kilograms is three\Nstandard deviations
Dialogue: 0,0:08:28.31,0:08:29.77,Default,,0000,0000,0000,,above the mean.
Dialogue: 0,0:08:29.77,0:08:34.10,Default,,0000,0000,0000,,So we want to know the\Nprobability of having a result
Dialogue: 0,0:08:34.10,0:08:36.25,Default,,0000,0000,0000,,more than three deviations\Nabove the mean.
Dialogue: 0,0:08:36.25,0:08:42.17,Default,,0000,0000,0000,,So that is this area way out\Nthere that I drew in orange.
Dialogue: 0,0:08:42.17,0:08:44.31,Default,,0000,0000,0000,,Maybe I should do it in\Na different color to
Dialogue: 0,0:08:44.31,0:08:45.28,Default,,0000,0000,0000,,really contrast it.
Dialogue: 0,0:08:45.28,0:08:48.58,Default,,0000,0000,0000,,So it's this long tail out\Nhere, this little small area.
Dialogue: 0,0:08:48.58,0:08:51.02,Default,,0000,0000,0000,,So what is that probability?
Dialogue: 0,0:08:51.02,0:08:53.42,Default,,0000,0000,0000,,So let's turn back to\Nour empirical rule.
Dialogue: 0,0:08:53.42,0:08:56.23,Default,,0000,0000,0000,,Well we know the probability--\Nwe know this area.
Dialogue: 0,0:08:56.23,0:08:59.74,Default,,0000,0000,0000,,We know the area between minus\Nthree standard deviations and
Dialogue: 0,0:08:59.74,0:09:01.96,Default,,0000,0000,0000,,plus three standard deviations.
Dialogue: 0,0:09:01.96,0:09:04.09,Default,,0000,0000,0000,,We know this-- since this is\Nlast the last problem I can
Dialogue: 0,0:09:04.09,0:09:08.20,Default,,0000,0000,0000,,color the whole thing in-- we\Nknow this area right here
Dialogue: 0,0:09:08.20,0:09:14.30,Default,,0000,0000,0000,,between minus 3 and plus\N3, that is it 99.7%.
Dialogue: 0,0:09:14.30,0:09:16.83,Default,,0000,0000,0000,,The bulk of the results\Nfall under there.
Dialogue: 0,0:09:16.83,0:09:17.94,Default,,0000,0000,0000,,I mean, almost all of them.
Dialogue: 0,0:09:17.94,0:09:20.32,Default,,0000,0000,0000,,So what do we have left\Nover for the two tails?
Dialogue: 0,0:09:20.32,0:09:21.22,Default,,0000,0000,0000,,Remember there are two tails.
Dialogue: 0,0:09:21.22,0:09:22.33,Default,,0000,0000,0000,,This is one of them.
Dialogue: 0,0:09:22.33,0:09:24.63,Default,,0000,0000,0000,,Then you have the results that\Nare less than three standard
Dialogue: 0,0:09:24.63,0:09:25.73,Default,,0000,0000,0000,,deviations below the mean.
Dialogue: 0,0:09:25.73,0:09:27.48,Default,,0000,0000,0000,,This tail right there.
Dialogue: 0,0:09:27.48,0:09:32.16,Default,,0000,0000,0000,,So that tells us that this,\Nless than three standard
Dialogue: 0,0:09:32.16,0:09:35.28,Default,,0000,0000,0000,,deviations below the mean and\Nmore than three standard
Dialogue: 0,0:09:35.28,0:09:39.15,Default,,0000,0000,0000,,deviations above the mean\Ncombined have to be the rest.
Dialogue: 0,0:09:39.15,0:09:46.53,Default,,0000,0000,0000,,Well the rest, there's only\N0.3% percent for the rest.
Dialogue: 0,0:09:46.53,0:09:48.25,Default,,0000,0000,0000,,And these two things\Nare symmetrical.
Dialogue: 0,0:09:48.25,0:09:49.62,Default,,0000,0000,0000,,They're going to be equal.
Dialogue: 0,0:09:49.62,0:09:54.88,Default,,0000,0000,0000,,So this right here has to be\Nhalf of this or 0.15% and
Dialogue: 0,0:09:54.88,0:09:59.16,Default,,0000,0000,0000,,this right here is\Ngoing to be 0.15%.
Dialogue: 0,0:09:59.16,0:10:03.65,Default,,0000,0000,0000,,So the probability of having a\None year old baby girl in the
Dialogue: 0,0:10:03.65,0:10:07.25,Default,,0000,0000,0000,,U.S. that is more than 12.8\Nkilograms if you assume a
Dialogue: 0,0:10:07.25,0:10:10.49,Default,,0000,0000,0000,,perfectly normal distribution\Nis the area under this curve,
Dialogue: 0,0:10:10.49,0:10:13.04,Default,,0000,0000,0000,,the area that is more than\Nthree standard deviations
Dialogue: 0,0:10:13.04,0:10:14.25,Default,,0000,0000,0000,,above the mean.
Dialogue: 0,0:10:14.25,0:10:21.76,Default,,0000,0000,0000,,And that is 0.15%.
Dialogue: 0,0:10:21.76,0:10:24.41,Default,,0000,0000,0000,,Anyway, I hope you\Nfound that useful.