Question

The heights of adult men in America are normally distributed with a mean of 69.5 inches and a standard deviation of 2.65 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 2.58 inches. (a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z = (b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = (c) Who is relatively taller? The 5 foot 11 inch American woman The 6 foot 3 inch American man

Answer #1

Solution :

a)

µ = 69.5

σ = 2.65

X =6 feet 3 inch = 6*12 + 3 = 75

Z =(X - µ ) / σ = ( 75 -
69.5 ) / 2.65

Z = 2.08

b)

µ = 64.1

σ = 2.58

( X = 5 feet 11 inch = 5*12+11 = 71.000 )

Z =(X - µ ) / σ = ( 71 - 64.1 )
/ 2.58

Z = 2.67

c)

The 5 foot11 inch American woman is relatively taller

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