Question

The typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. About 68% of adults typically sleep between a minimum of ___ hours a night and a maximum of ____ hours a night. Please enter your answer in the following format and round to the first decimal place: (min_value, max_value)

Answer 1

(6.2, 8.8).

Explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.5 hours

Standard deviation = 1.3 hours

About 68% ...

By the Empirical Rule, within 1 standard deviation of the mean.

7.5 - 1.3 = 6.2

7.5 + 1.3 = 8.8

So in the format requested

(6.2, 8.8).