The midterm exam scores of a STAT class are normally distributed with average score of 81 and a standard deviation of 6.5. (11 marks)

a. Define the variable X. (1 mark)

b. Find the probability that a random selected student scored above 73.2. (2

marks)

c. Determine and interpret the 87th percentile for the midterm exam scores. (3 marks)

d. If we randomly choose 25 students of the stat class, describe the sampling distribution of their average score. Please indicate shape, mean, and standard deviation. (3 marks)

e. For the randomly selected 25 students, find the probability that their average score is less than 77.1. Let variable x bar be the average score for the randomly selected 25 students