(4 points) The distribution of heights of adult men in the U.S. is approximately

Question

(4 points) The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about a normal distribution and the 68-95-99.7 rule to answer the following.

(a) About what percent of men are shorter than 66.5 inches?

A. 5% B. 16% C. 2.5% D. 32% E. None of the above.

(b) About what percent of men are taller than 74 inches?

A. 67% B. 2.5% C. 95% D. 5% E. None of the above.

(c) About what percent of men are between 64 and 66.5 inches?

A. 34%. B. 13.5%. C. 47.5%. D. 95%. E. None of the above.

(d) Between what approximate heights do the middle 95 percent of men fall?

A. 61.5 to 76.5 inches B. 69 to 74 inches C. 64 to 74 inches D. 66.5 to 71.5 inches E. None of the above.

Explanation / Answer

a) P(X < 66.5)

= P(z < (66.5 - 69)/2.5)

= P(z < -1)

= 16%

Option A is correct.

b) P(X > 74)

= P(z > 2)

= 2.5%

Option B is correct.

c) P(64 < X < 66.5)

= P(-2 < z < -1)

= 13.5%

Option B is correct.

d) As per empirical rule, middle 95% data lies between 2 SD from the mean.

So,

Approximate heights = (69 - 2*2.5) and (69 + 2*2.5) i.e. 64 and 74 inches

Option C is correct.

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