Question

The National Sleep Foundation recommends that adults between 18−6418-64 years of age sleep between 77 and 99 hours per night. A researcher collected data on the amount of sleep that students in college slept per night. The data were approximately normally distributed with the following mean and standard deviation

mean = 7.87.8 hours
standard deviation = 1.51.5 hours

Use this information and the online normal distribution calculator button below to answer the questions. Round your percents to two decimal places.

Note: Use z-scores rounded to two decimal places in your calculations to avoid roundoff errors.

Normal Calculator

What percent of students slept between 88 hours and 1010 hours? %

What percent of students slept less than 6.46.4 hours? %

What percent of students slept more than 10.110.1 hours? %

What percent of students slept less than 3.853.85 hours or more than 11.0511.05 hours ? %

Answer 1

percent of students slept between 8 hours and 10 hours is

P(8<X<10)
=P((8-7.8)/1.5<Z<(10-7.8)/1.5)
=P(0.13<Z<1.47)
=P(Z<1.47)-P(Z<0.13)
=0.9292-0.5517
=0.3775 (by using normal table)
=37.75%

percent of students slept less than 6.4 hours is

P(X<6.4)
=P(Z<(6.4-7.8)/1.5)
=P(Z<-0.93)
=0.1762 (by normal table)
=17.62%

percent of students slept more than 10.1 hours is

P(X>10.1)
=P(Z>(10.1-7.8)/1.5)
=P(Z>1.53)
=1-P(Z<1.53)
=1-0.937
=0.063 (by normal table)

percent of students slept less than 3.85 hours or more than 11.05 hours is

=1-P(3.85<X<11.05)
=1-P((3.85-7.8)/1.5<Z<(11.05-7.8)/1.5)
=1-P(-2.63<Z<2.17)
=1-(P(Z<2.17)-P(Z<-2.63))
=1-(0.985-0.0043)
=1-0.9807 (by using normal table)
=0.0193

=1.93%