Question

the heights of adult men in america are normally distributed, with a mean of 69.4 inches and a standard deviation of 2.64 inches. the heights of adult women in america are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.51 inches.
a. if a man is 6 feet 3 inches tall, what is his z - score (to 4 decimal places)?
z = 2.1212

b. if a woman is 5 feet 11 inches tall, what is her z - score (to 4 decimal places)?
z =
enter an integer or decimal number, accurate to at least 4 decimal places more...

c. who is relatively taller?
the 6 foot 3 inch american man
the 5 foot 11 inch american woman

Explanation:

Step1: Convert height to inches

6 feet 3 inches = 6×12 + 3 = 75 inches

Step2: Calculate z-score for man

$z = \frac{75 - 69.4}{2.64} = \frac{5.6}{2.64} \approx 2.1212$

Step1: Convert height to inches

5 feet 11 inches = 5×12 + 11 = 71 inches

Step2: Calculate z-score for woman

$z = \frac{71 - 64.1}{2.51} = \frac{6.9}{2.51} \approx 2.7490$

Step1: Compare z-scores

Man's z=2.1212, woman's z=2.7490; 2.7490 > 2.1212

Answer:

a. 2.1212
b. 2.7490
c. The 5 foot 11 inch American woman