Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100
(a) What is the probability that a randomly selected applicant scores 625 or more?
(b)What is the probability that a randomly selected applicant scores less than 500?
The shape of the normal distribution stays the same when the mean and standard deviation change (it moves left or right and it scales up or down). Probabilities for a standard normal distribution (called Z, or N(0,1)) with a mean of zero and a standard deviation of 1 are well known, so the first thing to do is to change your test scores into this standard form, in which case they are known as z-scores.
For part (a), you would subtract the mean of 500 to get 125, then divide by the standard deviation of 100 to get 1.25. You could then look up the probability that a standard normal random variable Z is > 1.25 (tables might give you the value for Z < 1.25, but you know that sum of probabilities of an event A or the opposite of event A happening add to 1, so you should still be able to get the answer you need).
Part (b) is similar.
