Question

The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. what is the expected number of students who had scores greater than 60?

Answer 1

23 students expected to have scores greater than 60.

Explanation:

60 is 2 standard deviations above the mean. This translates into a z-score of +2. According to a table of z-scores, the area under the standard normal curve to the left of z = 2 is 0.9772; that to the right of z = 2 is 1.0000 - 0.9772, or 0.0228. This 0.0228 represents the probability that a given score is greater than 60.

This fraction (0.0228) of 1000 students comes out to 23 (rounded up from 22.75).