Problem 7: (15 marks) The scores of students on the ACT (American College Testing)

college entrance examination in a recent year had the normal distribution with mean = 18

and standard deviation = 6. 100 students are randomly selected from all who took the test.

a. (4 marks) What is the probability that the mean score for the 100 students is between 17

and 19 (including 17 and 19)?

b. (7 marks) A student is eligible for an honor program if his/her score is higher than 25.

Find an approximation to the probability that at least 15 students of the 100 students

are eligible for the honor program.

c. (4 marks) If the sample size is 4 (rather than 100), what is the probability that more than

50% (not include 50%) students are eligible for the honor program?