Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. What is the probability that a randomly selected exam will have a score of at least 71?

  

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.

a. What is the probability that a randomly selected exam will have a score of at least 71?
b. What percentage of exams will have scores between 89 and 92?
c. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d. If there were 334 exams with scores of at least 89, how many students took the exam?