Question

2. Men who wish to join the new United States Space Force can't be too tall or too short. Suppose the Space Force wants to make sure that 95 percent of men are eligible on the basis of height. (Strictly speaking, I don't know what this percentage is but let's suppose it is 95%.) Assume male heights are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches,. Answer the following questions.

a) If the force accepts 95% of men based on height, what percentage of men will it reject because of failure to meet the height requirement?[1]

b) Find the percentile height for the minimum height? [4]

c)Find the percentile for the maximum height. [4]

d) Draw a picture of the normal curve with the appropriate mean and percentiles for the height requirement. [3]

Answer 1

Here mean height = = 69 inches

standard deviation = = 2.8 inches

(a) Here  95% of men based on height so percentage of men will it reject because of failure to meet the height requirement = 100 - 95 = 5%

(b) percentile height for the minimum height is 2.5%

z = -1.96

Minimum height = 69 - 1.96 * 2.8 = 63.51 inches

(c) percentile for the maximum height is 97.5%

Maximum Height = 69 + 1.96 * 2.8 = 74.49 inches