Question: Fifty students are enrolled in a Statistics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90.

a) Determine the standard error of the mean.

b) What assumption must be made before we can determine an interval for the mean grade of all the students in the class? Explain why.

c) Assume the assumption of part b is met. Provide a 90% confidence interval for the mean grade of all the students in the class.

d) If there were 200 students in the class, what would be the 90% confidence interval for the mean grade of all the students in the class?