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According to a National Health Survey, American men’s heights are normally distributed with a mean given by μ=69.7 inches and a standard deviation given by σ=2.8 inches. a). If a man is randomly selected, find the probability that his height is more 72 inches.

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Answer: 0.206

Step-by-step explanation:

Given that :

Height of American men is normally distributed :

Mean height (μ) = 69.7 inch

Standard deviation (σ) = 2.8 inch

Probability that height of a randomly selected man is more than 72 inches

P(X > 72)

Obtain the standardized score (Zscore):

Zscore = (x - μ) / σ

Zscore = (72 - 69.7) / 2.8

Zscore = 2.3 / 2.8

Zscore = 0.8214285

Zscore = 0.8214

Using the Z probability calculator ;

P(Z > 0.8214) = 0.20571

Probability of selecting a man whose height is more Than 72 is 0.206

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