The heights of adult men in America are normally distributed, with a mean of 69.
ID: 3149860 • Letter: T
Question
The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.56 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 6 foot 3 inch American man The 5 foot 11 inch American woman
Explanation / Answer
Normal Distribution
Mean ( u ) =69.3
Standard Deviation ( sd )=2.62
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
Z = (75-69.3)/2.62
Z = 5.7/2.62= 2.1756
b.
Mean ( u ) =64.2
Standard Deviation ( sd )=2.56
Normal Distribution = Z= X- u / sd ~ N(0,1)
Z = (71-64.2)/2.56
Z = 6.8/2.56= 2.6563
c.
The 5 foot 11 inch American woman is taller
since it has larger z value
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