The time taken to complete a maths exam is normally distributed with a mean of 108 minutes and a standard deviation of 15 minutes.

a. If a student is randomly selected from all students taking this maths exam, find the probability that this student will take more than 90 minutes to complete this maths exam. (3 marks)

b. If a student is randomly selected from all students taking this maths exam, find the probability that this student will take fewer than 105 minutes to complete this maths exam. (3 marks)

c. Suppose that we draw a random sample of 100 students from all students taking this maths exam. Find the probability that the average time taken of the 100 students will be more than 112 minutes. (4 marks)

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