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6.2 WS Z-Scores
Name:__________________________ #: _________
On one test your class achieved an average grade of 80 with a standard deviation of 8 points.
1. If you got a 96, what’s your z score?
2. Your best friend got a 76. What’s her z score?
3. What test grade has a z score of +1.5?
4. The teacher calls home whenever a student’s Z score is worse than -2.0. What grade earns you
that phone call home?
5. The men’s combined skiing event in the winter Olympics consists of two races: a downhill and a
slalom. Times for the two events are added together, and the skier with the lowest total time
wins. In the 2006 Winter Olympics, the mean slalom time was 94.2714 seconds with a standard
deviation of 5.2844 seconds. The mean downhill time was 101.807 seconds with a standard
deviation of 1.8356 seconds. Ted Ligety of the United States, who won the gold medal with a
combined time of 189.35 seconds, skied the slalom in 87.93 seconds and the downhill in 101.42
seconds. On Which race did he do better compared with the competition?
6. Your statistics teacher has announced that the lower of your two tests will be dropped. You got
a 90 on Test 1 and an 80 on Test 2. You’re all set to drop the 80 until she announces that she
grades “on a curve”. She standardized the scores in order to decide which the lower one is. If
the mean on the first test was 88 with a standard deviation of 4 and the mean on the second
was 75 with a standard deviation of 5. Which one will be dropped?
In Chapter 5 you made box plots for the number of calories and the fiber content in 23 kinds of Kellogg’s
cereals. Now let’s think about the sugar content. Those cereals average 7.6 grams of sugar per serving
with a standard deviation of 4.5 grams.
7. Find the z scores for the following cereals and describe what the Z score tells you about that
cereal.
a. Frosted Flakes: 11 grams of sugar per serving
b. Apple Jacks: 14 grams of sugar per serving
c. Crispix: 3 grams of sugar per serving
8. The Z score for Honey Smacks sugar content is a very high 3.87! How many grams of sugar are in
one serving?
9. Product 19 is very low in sugar, with a z score of -.8. How many grams are in a serving of this
cereal?
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