Question

The results of a national survey showed that on average, adults sleep 7.4 hours per night. Suppose that the standard deviation is 1.8 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 3.8 and 11 hours per day. Enter your answer as a percentage. %

Answer 1

Answer: 95%

Step-by-step explanation:

Given : The results of a national survey showed that on average, adults sleep $\mu=7.4$ hours per night.

Standard deviation: $s=1.8$ hours

a) To find : the percentage of individuals who sleep between 3.8 and 11 hours per day.

Note that $3.8=7.4-2(1.8)$

i.e. 3.8 is 2 standard deviations less than the mean value.

$11=7.4+2(1.8)$

i.e. 11 is 2 standard deviations more than the mean value.

According to the empirical rule , about 95% of the population falls within 2 standard deviation from the mean.

⇒ About 95% of individuals who sleep falls within 2 standard deviation from the mean i.e. between 3.8 and 11 hours per day .

Hence, the approximate percentage of individuals who sleep between 3.8 and 11 hours per day = 95%