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Answer: (a) 0.927
(b) 14.2%
Explanation:
Given : According to the National Health Survey, the heights of adult males in the United States are normally distributed .
Mean :
Standard deviation :
Let X be a random variable that represents the heights of adult males in the United States .
Z-score :
(a) For x= 64
For x= 74
Using the standard normal distribution table , we have
The deviation 2.8 inches. (a) What is the probability that an adult male chosen at random is between 64 and 74 inches tall :-
Hence, the probability that an adult male chosen at random is between 64 and 74 inches tall = 0.927
b) Since 1 feet = 12 inches
Then , 6 feet =
The z-score corresponds to x=72 :
Then , the probability that the adult male population is more than 6 feet tall :-
Hence, the percentage of the adult male population is more than 6 feet tall = 14.2%