# Z scores of the World's Tallest Women

1. Heights of Presidents. With a height of 67 in., William McKinley was the shortest president of the past century. The presidents of the past century have a mean height of 71.5 in. and a standard deviation of 2.1 in.

a. What is the difference between McKinley's height and the mean height of presidents from the past century?

b. B. How many standard deviations is that [the difference found in part (a)]?

c. Convert McKinley's height to a z score.

d. If we consider "usual" heights to be those that convert to z scores between -2 and 2, is McKinley's height usual or unusual?

2. World's Tallest Woman. Sandy Allen is the world's tallest woman with a height of 91.25 in. (or 7 ft. 7.25 in.). Women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in.

a. What is the difference between Sandy Allen's height and the mean height of women?

b. How many standard deviations is that [the difference found in part (a)]?

c. Convert Sandy Allen's height to a z score.

d. Does Sandy Allen's height meet the criterion of being unusual by corresponding to a z score that does not fall between -2 and 2?

https://brainmass.com/statistics/z-test/scores-worlds-tallest-women-238150

#### Solution Preview

Z scores

1. Heights of Presidents. With a height of 67 in., William McKinley was the shortest president of the past century. The presidents of the past century have a mean height of 71.5 in. and a standard deviation of 2.1 in.

a. What is the difference between McKinley's height and the mean height of presidents from the past century?

b. B. How many standard deviations is that [the difference found in part (a)]?

c. Convert McKinley's height to a z score.

d. If we consider "usual" heights to be those that convert to z scores between -2 and 2, is McKinley's height usual or unusual?

2. World's Tallest Woman. Sandy Allen is the world's tallest woman with a height of 91.25 in. (or 7 ft. 7.25 in.). Women have heights with a mean of 63.6 in. and a standard deviation of 2.5 in.

a. What is the difference between Sandy Allen's height and the mean height of women?

b. How many standard deviations is that [the difference found in part (a)]?

c. Convert Sandy Allen's height to a z score.

d. Does Sandy Allen's height ...

#### Solution Summary

The solution examines the data from the World's Tallest Women. The Z scores determined.