Question: #12 Scores for men on the verbal potion of the SAT test normally distributed with a mean of 509 and a standard deviation of 112. Based on data from the College Board randomly selected men are given a review course before taking the SAT test. Assume that the course has no affect.

a) If one of the men is randomly selected find the probability is at least 590.

b) If 16 men are selected find the probability that their mean score is at least 590.

c) In finding the probability of part b why can the central limit theorem be used even thought the sample size does not exceed 30

d) If the random sample of 16 men does result does result in a mean score of 590 is there strong evidence to support that the claim that the course is actually effective. Why or why not.