00:01
For this problem, for part a, we would have that we would expect our p hat value, or the average of the p hat values, to be equal to the population proportion, which we're told is equal to 0 .32.
00:14
For part b, we'd have that the standard deviation of our sample proportions is going to be equal to the square root of our population proportion times one minus the population proportion divided by our sample size.
00:29
In this case, that's the square root of 0 .32 times 1 minus 0 .32 divided by n is 309.
00:44
And so we should find that the standard deviation of the sample proportions is equal to roughly 0 .0265.
00:53
Then for part c to find the probability of p hat being between 0 .3 and 0 .3, let me double check the calculation there.
01:07
Pardon me, 0 .3 and 0 .34.
01:10
What we can do is find the probability of p hat being between the different corresponding z scores, where the z score is going to be given by, for instance, for the z score of 0 .3, that would be, be given by 0 .3 minus 0 .32 divided by our standard deviation, 0 .0265, which would give a result of negative 0 .7547.
01:41
And we'd have that 0 .34.
01:44
It's the same amount or same distance above the mean value.
01:48
So we would have that the corresponding z scores would be 0 .7 or negative 0 .7547 for the lower bound and positive 0 .7547 for the upper bound...