Answer: 95%
Step-by-step explanation:
Given : The results of a national survey showed that on average, adults sleep [tex]\mu=7.4[/tex] hours per night.
Standard deviation: [tex]s=1.8[/tex] hours
a) To find : the percentage of individuals who sleep between 3.8 and 11 hours per day.
Note that [tex]3.8=7.4-2(1.8)[/tex]
i.e. 3.8 is 2 standard deviations less than the mean value.
[tex]11=7.4+2(1.8)[/tex]
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%
