Question

# The heights of adult men in America are normally distributed with a mean of 69.5 inches...

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

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

Thank you so much

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