An economics professor states on her syllabus that final grades will be distributed using the normal distribution. The final averages of 300 students are calculated, and she groups the data into a frequency distribution as shown in the accompanying table. The mean and the standard deviation of the final are x = 72 and s = 10.

Final Ave rages ........................... Frequency

F: Less than 50 ............................... 5

D: 50 up to 70 ............................. 135

c: 70 up to 80 .............................. 105

B: 80 up to 90 .............................. 45

a: 90 or above .............................. 10

....................................... total = 300

a. Using the goodness-of-fit test for normality, state the competing hypotheses in order to determine if we can reject the professor's normality claim.

b. At a 5% significance level, what is the critical value?

c. Calculate the value of the test statistic.

d. What is the conclusion to the test?