The heights of adult men in America are normally distributed, with a mean of 69.
ID: 3371312 • Letter: T
Question
The heights of adult men in America are normally distributed, with a mean of 69.6 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 64.4 inches and a standard deviation of 2.53 inches. a) If a man is 6 feet 3 inches tall, what is his z- score (to two decimal places)? b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent. e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a meaningful sentence.Explanation / Answer
a)as z score =(X-mean)/std deviation
hence z =(75-69.6)/2.64=2.05
b)
P(Z<2.05)=98.0%
c)
z scsore =(71-64.4)/2.53=2.61
d)
P(Z>2.61)=0.5%
e)
as z score for a 5'11'' women is higher; she should be relatively taller
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