24. An economics professor states on her syllabus that final grades will be d istributed using the normal distribution. The final averages o f 300 students are calculated, and she groups the data into a frequency d istribution as shown below.The mean and the standard deviation of the final averages are Final Averages Observed 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. Calculate the value o f the test statistic.

c. At a 5% significance level, w hat is the critical value?

d. What is the conclusion to the test?