An observed frequency distribution of exam scores is as follows:

Exam score Under 60  60-69  70-79  80-89  90-100

Frequency      30            30      140       60        40

(a) Assuming a normal distribution with μ = 75 and σ = 15, find the probability of a randomly selected subject belonging to each class. (Use boundaries of 59.5, 69.5, 79.5, 89.5, 100.)

(b) Using the probabilities found in part (a), find the expected frequency for each category.

(c) Use a 0.05 significance level to test the claim that the exam scores were randomly selected from a normally distributed population with μ = 75 and σ = 15.