00:01
So it tells us that it's normally distributed with a mean of 85 and a standard deviation of 21 .25.
00:12
Remember, your z scores are always x minus the mean divided by the standard deviation.
00:17
So in part a, we want the probability that x is greater than 95 for any interval, which is the probability that z is greater than 0 .4706, which by my calculator is 0 .31896.
00:36
In b, we want a sample of those to be 20 intervals.
00:43
So our sampling distribution has the mean that's the mean given to 85, and our standard deviation is the standard error.
00:53
The standard deviation divided by the square root of n, or 21 .25 divided by the square root of 20, which is 4 .751 .7 .1.
01:02
Rounded to four decimal places and we wanted the probability that x bar was greater than 95 which means z is greater than 2 .1045 which by my calculator is 0 .075 which by my calculator is 0 .0176674 c our sample size increased to 30 our mean stayed the same at 85 our standard d deviation is 21 .25 divided by the square root of 30 or 3 .8797.
01:48
So we want the probability that x bar is greater than 95 again, which is the probability that z is greater than 2 .5775 or 0 .004976.
02:03
So as the sample size increases, the probability of the sample mean is decreasing...