This problem also requires you to use the z score

like you did in Problem 16. This problem also comes from Section. You will need to use a table of z scores (supplied on the Final Exam) to do part c.

**Problem 17** Suppose the mean score on a test is 76 with a standard deviation of 8.

a. What is the z-score for a student who scored a 90 on the test?

**Solution**

b. What test score corresponds to a z-score of –0.35?

**Solution** In part a, you were given a data value and asked to find the z score. This problem does the opposite. Put the values into the z score formula:

c. If the test scores are normally distributed, then what percent of the students would score between 80 and 89 on the test?

**Solution** Graphically, we are trying to determine the portion of area under a bell curve from 80 to 89.

To get areas, we need to calculate the z values and read the area from the z table formula.

For a score of *x* = 80,

And for *x* = 89,

A z score of 0.5 corresponds to an area of 0.192 from the mean of 76 to 80. A z value of 1.63 corresponds to an area of .449 from the mean of 76 to 89. The area between 80 and 89 is the difference between these areas or .449 – .192 or .257.