Chapter 7, Problem 10PS

According to the National Survey of Student Engagement, the average spends about 15 hours each week preparing for classes; preparation for classes includes homework, reading and any other assignments.

Assume the standard deviation of time spent preparing for classes is 4 hours. If you select a random sample of 16 students,

a. what is the probability that the mean time spent preparing for classes is at least 14 hours per week?

b. there is an $85\%$ chance that the sample mean is less than how many hours per week?

c. What assumption must you make in order to solve (a) and (b)?

d. If you select a random sample of 64 students, there is an $85\%$ chance that the sample mean is less than how many hours per week?