Big stats course STA220H is a large introductory Statistics course at the University of Toronto, with 720 students enrolled. On the term test, the average score was 72, with a standard deviation of 16.

There are 24 tutorials, with 30 students in each. Xiu Xiu teaches one, and Sabri teaches another. Assume that tutorial groups are formed quite randomly.

a) We select a student at random from Sabri’s tutorial. Find the probability that this student’s test score is at least 80.

Assume that scores are Normally distributed.

b) We select one student at random from each tutorial. Find the probability that Sabri’s student outperformed Xiu Xiu’s student by at least seven marks on the test. (Hint: Work with the difference between the two scores.) Assume that scores are Normally distributed.

c) What is the probability that the average for Sabri’s tutorial is at least 80? Do you need to assume that scores are Normally distributed?

d) What is the probability that the average test score in Sabri’s tutorial is at least seven marks higher than the average test score for Xiu Xiu’s tutorial? (Hint: Work with the difference between the two tutorial averages.) Do you need to assume that scores are Normally distributed?