Question

The mean hours of sleep that students get per night is 5 hours, the standard deviation of hours of sleep is 1 hour, and the distribution is approximately normal. Complete the following sentence.For about 68% of students, nightly amount of sleep is between ______and _____ hours.For about 95% of students, nightly amount of sleep is between ______and _____ hours.For about 99.7% of students, nightly amount of sleep is between ______and _____ hours.

Answer 1

.For about 68% of students, nightly amount of sleep is between __4____and ___6__ hours.For about 95% of students, nightly amount of sleep is between __3____and __7___ hours.For about 99.7% of students, nightly amount of sleep is between ___2___and __8___ hours.

Explanation:

The empirical rule tells us that for normal distributions,

68% of data lie within one standard deviation of the mean.

Thus, 68% of data lie within
`\bar{x} \pm s`

⇒ 5 ± 1 = (4, 6) hours

Similarly, 95% of data lie within two standard deviation of the mean.

Thus, 95% of data lie within
`\bar{x} \pm 2s`

⇒ 5 ± 2 = (3, 7) hours

99.7% of data lie within one standard deviation of the mean.

Thus, 99.7% of data lie within
`\bar{x} \pm s`

⇒ 5 ± 3 = (2, 8) hours