According the course handbook at a large university, the length of classes held on Monday (M), Wednesday (W), and Friday (F) have a mean of 50 minutes and standard deviation of 5 minutes. The length of classes held on Tuesdays (T) and Thursdays (R) have a mean of 75 minutes and standard deviation of 7 minutes. The college provost is concerned that professors that teach classes on Tuesdays and Thursdays are dismissing their students too early. To determine if there is credibility about this concern the provost selects a random sample of 30 TR classes and 30 MWF classes and determines the length of each class. Let XTR - Fwf be the difference in the sample mean class length for the two types of classes. (a) What is the shape of the sampling distribution of xTr – xwf? Why?
(b) Find the mean of the sampling distribution.
(c) Verify that the 10% condition is met, then calculate the standard deviation of the sampling distribution.
(d) What is the probability that the difference in sample means is less than 20 minutes?