Question

A study found that the heights of college males follow a normal distribution with a mean of 70 inches with a standard deviation of 2.5 inches. What is the probability that randomly selected male student will be between 68 and 77 inches​ tall? A. 3.60 B. 0.2119 C. 0.6580 D. 0.7855

Answer 1

Given = 70, = 2.5

To find the probability, we need to find the z scores.

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For P (68 < X < 77) = P(X < 77) – P(X < 68)

For P( X < 77)

Z = (77 – 70)/2.5 = 2.8

The probability for P(X < 77) from the normal distribution tables is = 0.9974

For P( X < 68)

Z = (68 – 70)/2.5 = -0.8

The probability for P(X < 68) from the normal distribution tables is = 0.2119

Therefore the required probability is 0.9974 – 0.2119 = 0.7855 (Option D)

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