00:01
We are looking at a normal distribution with a population mean mu of 27 .9, a standard deviation sigma of 60 .7.
00:10
But we're taking a sample of n equals 23.
00:14
So we're not looking at individual values.
00:16
Well, we actually are in part a, but for part b we'll be looking at this sample.
00:21
So i'll draw a normal distribution to help us out with part a.
00:26
Total area under this curve is 1, or 100 % of the probability, and it's symmetric.
00:34
So to the left of the mean is 0 .5, right to mean 0 .5.
00:39
So our first step to finding the probability is to find the z score.
00:45
Z is x minus mu over sigma.
00:49
And here x is 49 .4.
00:52
So that's above the mean.
00:55
And we want less than.
00:57
So area to the left.
00:59
Okay, so z is 49 .4 minus 27 .9.
01:10
So that is 21 .5 divided by 60 .7.
01:21
Which isn't a great number, so i'm just going to leave it in exact form...