Question

The times that college students spend studying per week have a distribution skewed to the right with a mean of 8.7 hours and a standard deviation of 2.2 hours. Find the probability that the mean time spent studying per week for a random sample of 45 college students would be a. between 8.3 and 8.9 hours.

Answer 1

Solution:
Given in the question
Mean = 8.7 hours
Standard deviation = 2.2
No. of samples = 45
We need to calculate P(8.3<Xbar<8.9) = P(Xbar<8.9) - P(Xbar<8.3)
Z = (8.9-8.7)/2.2/sqrt(45) = 0.2/ 0.3279 = 0.61
Z = (8.3-8.7)/2.2/sqrt(45) = -0.4/0.3279 = -1.22
From Z table we can find p-value
P(8.3<Xbar<8.9) = 0.7291- 0.1112 = 0.6179

So there is 61.79% that the mean time spent studying per week for a random sample of 45 college students would be between 8.3 and 8.9 hours