Scores on a test are normally distributed with a mean of 80 and a standard deviation of 5. what is the probability that a randomly selected student scored between 85 and 91?

Because the mean, standard deviation, and student scores are given, you use the formula:   to determine the z score for each scores.  Then look up these z scores in a cumulative z score table, to find the probabilities associated with each of them.  Subtract the lower probability from the higher probability and find the final answer.  

For this problem: = 2.2 and = 1.

The probabilities associated with these z scores are: 0.9861 and 0.8413 respectively.  Therefore the probability that a randomly selected student scores between 85 and 90 = 0.9861 - 0.8413 = 0.1448 or 14.48 %

Jeff Negus
Tutoring In An Instant (TutIAI)