A study found that the heights of college males follow a normal distribution with a mean...

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

Solutions

Expert Solution

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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orchestra answered 1 year ago

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