# Standard Scores and Percentiles

1. Heights of American Men. The heights of American adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.7 inches. (Use Table 6.3 on page 390 of your e-text to find the Percentile based on the z-score that you calculate.)

a. What are the standard score and percentile of a height of 72 inches?

b. What are the standard score and percentile of a height of 66 inches?

c. What percentage of the American adult male population is taller than 6'4"?

d. What percentage of the American adult male population is shorter than 5'4"?

e. Assume that the American population consists of 114 million adult men. Approximately how many men are at least as tall as the basketball player Kobe Bryant, who is 6'7" tall?

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#### Solution Preview

1a

standard score = (72 - 69.7) / 2.7 = 0.85

From the z-table, locate the standard score to find the percentile.

Percentile = 80th percentile.

b

standard score = (66 - 69.7) / 2.7 = -1.37

From the z-table, ...

#### Solution Summary

Computations are shown for each answer. Please refer to corresponding values on the z-table.