Question

The results of a national survey showed that on average, adults sleep 7.4 hours per night. Suppose that the standard deviation is 1.1 hours and that the number of hours of sleep follows a bell-shaped distribution. If needed, round your answers to two decimal digits. If your answer is negative use “minus sign”.

(a) Use the empirical rule to calculate the percentage of individuals who sleep between 5.2 and 9.6 hours per day. Enter your answer as a percentage. %

(b) What is the z-value for an adult who sleeps 8 hours per night?

(c) What is the z-value for an adult who sleeps 6 hours per night?

Answer 1

Hello there,

Here μ = 7.4 hours per night and σ = 1.1 hours per night

(a) Approximately 95% of the data falls within two standard deviations of the mean (or between the mean – 2 times the standard deviation, and the mean + 2 times the standard deviation). The mathematical notation for this is: μ ± 2σ.

μ ± 2σ = (5.2, 9.6).

Hence, we conclude that 95% of individuals sleep between 5.2 and 9.6 hours per day.

z-value is calculated as z = (x - μ) / σ

(b) Here, x = 8 hours per night

z = 0.5455

(c) Here, x = 6 hours per night

z = -1.2727