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MCTC Intro Stats
5.2 Even More Normal Calculations with Z-scores Classwork
1. A normal distribution of scores has a standard deviation of 10. Find the z-scores corresponding to each of
the following values:
a) A score that is 20 points above the mean.
b) A score that is 10 points below the mean.
c) A score that is 15 points above the mean.
d) A score that is 30 points below the mean.
2. For the z-score below, find the percentile (percent of individuals scoring at or below):
z = – 2.24
3. For the z-score below, find the proportion of cases falling above the z:
z = – 2.07
4. For the z-score below, find the area between the mean and the z-score:
z = 1.17
5. On the driving range, Tiger Woods practices his swing with a particular club by hitting many, many balls.
Suppose that when Tiger hits his driver, the distance the ball travels follows a Normal distribution with
mean 304 yards and standard deviation 8 yards.
a) What percent of Tiger’s drives travel at least 290 yards?
b) What percent of Tiger’s drives travel between 305 and 325 yards?
c) How far would Tiger need to hit the ball to be in the longest 20% of his drives?
6. Hershey's chocolate making machines produce chocolate bars with weights that are approximately Normally
distributed with  = 200g and  = 8g. They will not allow chocolate bars to be sent to distributors if they are
in the top 5% of weights. What is the maximum weight of a Hershey's chocolate bar that you could buy
from a store?
7. A few years ago, my friend took the ACT for college admission and scored 24. The same friend also took
the SAT and scored 1100. He wants to know if he did better on the ACT or the SAT. ACT scores that year
fell between 0 and 36, with a mean of 21 and a standard deviation of 5. SAT scores that year were between
200 and 1600, with a mean of 1000 and a standard deviation of 200. On which exam did my friend perform
better?