Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed.
a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement.
b. If 4 randomly selected adults take the Wechsler IQ test, find the probability that their mean score is at least 131.
c. If 4 subjects take the Wechsler test and they have a mean of 132 but the individual scores are lost, can we conclude that all 4 of them are eligible for Mensa?