The number of copies made each week by teachers at Lamley High School follows a bell-shaped distribution with a
mean of 550 copies and a standard deviation of 185 copies. Mr. Thomas made 782 copies last week. His Z-score is
1.25. Which of the following statements best interprets this value?
O Mr. Thomas made 125 more copies, on average, than the mean number of copies of teachers at Lamley High
School.
O The number of copies Mr. Thomas made is 1.25 standard deviations less than the mean number of copies of
teachers at Lamley High School.
O The number of copies Mr. Thomas made is 1.25 standard deviations more than the mean number of copies of
teachers at Lamley High School.
O The number of copies Mr. Thomas made is 1.25 standard deviations less than the median number of copies of
teachers at Lamley High School.
O The number of copies Mr. Thomas made is 1.25 standard deviations more than the median number of copies of
teachers at Lamley High School.

In statistics, a z-score is measurement that describes a value's relationship to the mean and allows us to compare the value and the mean. It tells us how many standard deviations above or below the population mean.

Mr. Thomas has a z-score of 1.25.

He made 782 copies last week. The statistic this is being compared to is the mean of 550 copies by teachers per week at Lamley High School.

Therefore, the best interpretation is Mr. Thomas made 1.25 standard deviations more than the mean number of copies. The correct answer is choice 3.

Let's make sure the other choices are incorrect.

The first answer is incorrect because a z-score doesn't compare the exact values, but uses the standard deviation to compare.
The second answer is incorrect because he made 782 copies, while the mean was 550. He made more copies, plus the z-score is positive.
The fourth and fifth answers are incorrect because the z-score doesn't use the median to compare.