Question

A large population of male college students had a nightly sleep time on Monday through Thursday that is normally distributed with a mean of 6.1 hours and a standard deviation of 1.9 hours.

a. If one of these students is selected at random, what is the probability that he has a mean sleep time less than 7 hours?

b. If a sample of 30 of these students is chosen, what is the probability that their mean sleep time is less than 7 hours?

Answer 1

Given = 6.1 and = 1.9

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

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(a) n = 1, For P( X < 7)

Z = (7 – 6.1) / [1.9 / sqrt(1)] = 0.47

The required probability from the normal distribution tables is = 0.6808

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(a) n = 30, For P( X < 7)

Z = (7 – 6.1) / [1.9 / sqrt(30)] = 2.59

The required probability from the normal distribution tables is = 0.9952

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