Question

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. In a group of 230 tests, how many students score above 96?

Answer 1

We are given with a mean of 76 and a standard deviation of 10. IN this case, we are asked to determine the probability that the score is beyond 96. 

z score = (96-76)/ 10 = 2

With the z-score of 2, the probability that is equivalent is 0.0235 or 2.35 percent. 

Answer 2

The score of 96 is 2 standard deviations above the mean score. Using the empirical rule for a normal distribution, the probability of a score above 96 is 0.0235.
Therefore the number of students scoring above 96 is given by:
$230\times 0.0235=5\ students$