In 2021, the final results for a Probability exam were normally distributed with a mean of 78% and a standard deviation of 15.

Required:

Show workings for each.

a. What is the probability of getting a mark of 68% or more? (2 marks)

b. What is the probability of getting a mark between 53% and 60%? (3 marks)

c. If the bottom 5% failed, what was the mark you need to receive to pass (see diagram)? (4 marks)