I broke down this question into two seperate questionsThere

(I broke down this question into two seperate questions.There is one more part, part d to it.)

http://www.chegg.com/homework-help/questions-and-answers/one-measure-quality-education-provided-university-number-students-per-class-president-larg-q7285713

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) Construct a stemplot for these data. What is the shape of the data distribution?

(c) 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.

Solution

a) In a normal distirbution mean median and mode are equal. But by seeing the data e understand that median is somewhere near 27 and mean is around 32 or 33. Hence the distribution is not normal.

b)

The distribution is positively skewed.

c) The sample size is large. So by unsing the central limit therom, we can use the inference methods.