00:01
We're looking at a normal distribution, so i'll start by drawing it.
00:09
The mean, mu, is 64 .4 inches.
00:15
The standard deviation sigma is 2 .72.
00:19
So like any probability curve, the area under this normal distribution is 1, and it is symmetric, so the area to the left of the mean is 0 .5, right of the mean, 0 .5.
00:31
We want to find, in part a, the 95th percentile.
00:36
So this is a cutoff point here, p95, where 95 % of women will be shorter, 5 % will be taller.
00:45
So to find this, we start by finding the corresponding z score.
00:50
So we're going to go from probability, area under the curve, to the z score, and then to height.
00:57
So to start off, what do we put into our table? so assuming this is the standard normal table, so you have z scores along the columns and and probabilities in the middle, and the standard table gives you the area between your cutoff point x and mu the mean.
01:19
So it gives you this area here.
01:23
Well, this area is going to be 0 .45.
01:27
If all of this is 0 .95, and this is 0 .05, this bit here is 0 .45.
01:34
So we look in the table, 0 .45, or as close as we can get, and this is 0 .05, and this bit here is 0 .45, and we look in the table, 0.
01:40
And that will give us the z score by matching up to the rows and columns.
01:47
So let's look at the table, looking for 0 .45, and okay, so it's exactly between two values, 1 .64 and 1 .65, which gives us the z score as 1 .645, as it's right between them.
02:11
Okay, so this tells us how many standard deviations away from a mean our value is...