One measure of the quality of education provided by a university is the number of
students per class. The president of a large university would like to estimate the true
mean size of all third-year classes at the university. A random sample of 30 third-year classes is selected. The number of students in each of the classes are ordered and shown below:

10 11 14 14 15 17 18 20 22 22
22 23 26 26 27 28 31 33 34 34
36 42 44 49 50 55 62 68 77 82

From these data, the sample mean is calculated to be 33.73. The population standard deviation of class sizes is known to be 18.50.

(a) Before even looking at the data, we know that the distribution of class sizes could
not possibly be normal. Explain why.

(b) It is clear that class size does not follow a normal distribution. Explain why it is still appropriate to use inference methods which rely on the assumption of normality.