Question

The distribution of hours of sleep per week night, among college students, is found to be Normally distributed, with a mean of 7.5 hours and a standard deviation of 0.75 hours (or 45 minutes). Use this information and the 68– 95– 99.7 rule to answer the following questions.

A) Draw the distribution, show where the mean is and show on the x-axis the points that correspond to one and two standard deviations from the mean

B) What range contains the middle 68% of hours slept per week night by college students?

C) What percentage of college students sleep more than 8.25 hours (or 8 hours and 15 minutes)? Use table B at the end of the book to answer the following questions

D) What percentage of students sleep less than 7 hours? E) What percentage of students sleep more than 8 hours? F) How long do the top 10% of sleepers sleep?

Answer 1

Solution:

mean=7.5

mean-sd=7.5-*0.75=6.75

mean+sd=7.5+*0.75=8.25

mean-2sd=7.5-2*0.75=6

meaan+2sd=7.5+2*0.75=9

B) What range contains the middle 68% of hours slept per week night by college students?

range is from 6.75 to 8.25 hours which is 68% of hours slept per week night by college students

that is 68% of hours slept per week night by college students lies in between 6 .75 and 8.25 hours

C) What percentage of college students sleep more than 8.25 hours (or 8 hours and 15 minutes)? Use table B at the end of the book to answer the following questions

Above 8.25=

13.5+2.35+0.15

=16%

P(X>8.25)=0.16

16%

D) What percentage of students sleep less than 7 hours?

percentage of students sleep less than 7 hours=0.15+2.35+13.5+9=25%

What percentage of students sleep more than 8 hours

percentage of students sleep more than 8 hours=0.15+2.35+13.5+9=25%

F) How long do the top 10% of sleepers sleep?

ANSWER"

8,46 hours