Question

Question 5 Use the following information to determine your answers: 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 random variable:

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 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% of adults:

Within 1 standard deviation of the mean. So

7.5 - 1.3 = 6.2 hours

7.5 + 1.3 = 8.8 hours.

So the answer is (6.2, 8.8).