Scores from an exam are normally distributed with a mean of 76 and a standard deviation of 10. Suppose 230 students take the exam. About how many would receive a score below 66?
First, determine the number of standard deviations that data score of 66 is from the mean.
To determine the x-axis values, subtract the standard deviation from the mean 76 repeatedly.
76 − 10 = 66
66 − 10 = 56
56 − 10 = 46
The scores that are below 66 are −2 and −3 standard deviations from the mean.
Add the percentages.
2.5% + 13.5% = 16%
About 16% of the scores are less than 66. Now find 16% of 230 students.
