Scores on an examination are assumed to be normally distributed with a mean of 78 and a variance of 36.

a. What is the probability that the person taking the examination scores higher than 72?
b. Suppose the students scoring in the top 10% of the distribution are to receive an A grade. What is the minimum score that the student must achieve to earn an A?
c. What must the cut-off point be for passing the examination if the examiner wants only the top 28.1% of all scores to be passing?
d. Approximately what proportion of students have scores 5 or more points above the score that cuts off the lowest 25%.
f. If it is known that the students score exceeds 72, what is the probability that his score exceeds 84?