A civil service exam is given to 200 job applicants. In recent years, grades have followed a normal distribution with mean 66.5 and variance 100. The grades of the job applicants are distributed as follows:

Grades Observed Frequency
Under 49.5 22
49.5 - 59.5 38
59.5 - 69.5 56
69.5 - 79.5 50
79.5 and over 34

a) Graph the observed frequencies on a histogram. Does the histogram appear to have the shape of a normal distribution with mean 66.5 and variance 100?

b) Test the hypothesis that the data came from a normal distribution with mean 66.5 and variance 100. Use a 5% level of significance.