4.On a test given to large number of students, the distribution of scores was found to be approximately normal with a mean of 72.53 points.

(a) If the probability is 0.90 that the mean score for a random sample of 10 students who took this test would be no more than 76 points, what was the standard deviation for the scores of all students who took the test?

(b) Based on your answer to part (a) above, what is the variance for the sampling distribution of x for a sample size of n = 25.

(c) Compared to a sample of size n = 25, would the variance of the sampling distribution for a sample of size n = 50 be larger or smaller? Discuss how you can determine this answer without completing any additional calculations.