Subject: Mathematics    / Statistics
Question

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).

a. For a randomly selected adult, find the probability of an IQ greater than 70.

b. Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range).

c. Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal range).

d. Find the first quartile, Q1, which is the IQ score separating the bottom 25% from the top 75%.

e. Mensa International calls itself “the international high IQ society,” and it has more than 100,000 members. Mensa states that “candidates for membership of Mensa must achieve a score at or above the 98thpercentile on a standard test of intelligence (a score that is greater than that achieved by 98 percent of the general population taking the test).” Find the 98thpercentile for the population of the Wechsler IQ scores. This is the lowest score meeting the requirement for Mensa membership.