The scores upon an admission test the Engineering Program of a certain university are normally distributed with a mean of 500 and a standard deviation of 100.
a) What is the probability that a randomly selected student will obtain a score of more than 605?
b) What is the score that separates the top 33% from the lower 67%?
c) What is the probability that the average score of a random sample of 9 students will be more than 605?
d) Why is a sample size of 9 sucient for the solution in part c to be valid?