00:01
So in this question we're told that the proportion p in the population is 0 .82, then we sample 100 americans and we want to get the sampling proportion p -hat.
00:22
Well, we know that p -hat will have a normal distribution, which will be centered on p, and which will have a variance p 1 minus p over n.
00:35
So this is the mean of p -hat, and this is the variance of p -hat.
00:44
Now we need to...
00:46
So this only holds if the success -failure criteria hold.
00:51
So the success -failure criteria is that n p should be greater than 10 and n 1 minus p should be greater than 10.
01:06
Well, in this case n p is 82, so that's all good, and n 1 minus p is 18, so that's good too.
01:21
So that allows the normal approximation to hold valid.
01:35
Okay, so now part b, in the sample obtained in part a, what's the probability that the proportion will exceed 0 .85? well, let's recall that z -scores are going to be given by p -hat minus p divided by the square root of p 1 minus p over n, and these are going to be our standard normal variables.
01:58
Now what's the probability that p -hat exceeds 0 .85? well, that's the probability of getting a z -score which exceeds...