Question 5.93
63. The Boston Beanstalks Club is a social club for tall people. To join the club, women must be at least 5 feet 10 inches (70 inches) and men at least 6 feet 2 inches (74 inches). Both men’s and women’s heights are approximately normally distributed, but from different normal distributions. You can compare observations from different normal distributions if you measure in standard deviations away from the mean, which converts the observation to a z-score. To compute an observation’s -score, subtract the mean and then divide the result by the standard deviation:
- Assume that women’s heights follow an approximately normal distribution with inches and inches. How many standard deviations above the mean must a woman be in order to join the Boston Beanstalks?
- Assume that men’s heights follow an approximately normal distribution with inches and inches. How many standard deviations above the mean must a man be in order to join the Boston Beanstalks?
- In terms of joining the Boston Beanstalks, which is more stringent, the height requirements for women or the height requirements for men? Explain.
63.
(a) . A woman's height must be 1.48 standard deviations above the mean height for women in order to join the Boston Beanstalks.
(b) . A man's height must be 0.98 standard deviations above the mean height for men in order to join the Boston Beanstalks.
(c) The height requirements for women are more stringent than for men. Women need to be a half standard deviation further from the mean than their male counterparts.