A New York Times review of the book The State Boys Rebellion by Michael D'Antonio cites this chilling quote: "to make sure every last moron was captured, many states, including Massachusetts, would establish traveling 'clinics' to administer IQ tests at public schools." The review mentions that by 1949, approximately 150,000 Americans were institutionalized.

a. The U.S. population in 1949 was about 150,000,000. What proportion of all Americans were institutionalized at that time?

b. Scores for the Wechsler IQ test are normal with mean 100 and standard deviation 15. Use the 68-95-99.7 Rule to sketch a curve for this distribution, marking off the scores that are within 1, 2, and 3 standard deviations of the mean.

c. Apparently, people were being institutionalized in the 1940s if their IQ was approximately how many standard deviations below the mean?

d. The reviewer cites that of the 150,000 institutionalized Americans at that time, an estimated 12,000 were in fact "of relatively normal intelligence." Discuss the harmful consequences of using the results of an IQ test to institutionalize people who, in fact, are capable of functioning normally in society.

e. Discuss the harmful consequences of failing to institutionalize people who are unable to function in society.