1.

For a normal distribution, whatz-score values form the boundaries that separate the middle 50% of the distribution from the rest of the scores?

2.

Mensa is an international high IQ society that accepts into its membership only those who score within the top 2% of the population on an approved intelligence test. Suppose that the scores on a Mensa-approved test are normally distributed with a population mean of 240 and a standard deviation of 30. What is the minimum score on this test that would qualify one for Mensa membership?

3.

The height of American men is normally distributed with a mean of 5'10" (or, in inches, 70") and a standard deviation of 3".

a. Actor George Clooney is 5'11" (71") tall. What proportion of American men is shorter than George Clooney?

b. R&B singer Usher is shorter than the mean by 0.5 standard deviations. What proportion of American men is shorter than Usher?

c. What is the height in inches that defines the shortest 10% of the American male population?

d. What proportion of American men stand within 1.5 standard deviations above and below the mean height?

e. What proportion of American men are between 72" and 75" tall?

f. CHALLENGE QUESTION: What are the heights in inches that define themost extreme8% of the population of American men? (HINT: Consider what it means to be "most extreme.")