The heights of women aged 20 to 29 are approximately Normal

The heights of women aged 20 to 29 are approximately Normal with mean 63 inches and standard deviation 2.6 inches. Men the same age have mean height 70 inches with standard deviation 2.7 inches.

(a) What is the z-score for a woman who is 6 feet tall? Please use 2 decimal places.
  

(b) What is the z-score for a man who is 6 feet tall? Please use 2 decimal places.

Solution

a)

A 6-ft woman is 72-in tall.

As

z = (x - u) / sigma

z = (72 - 63) / 2.6 = 3.46 [answer]

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b)

Now, using the u and sigma values for men,

z = (72-70)/2.7 = 0.74 [answer]