Z-Scores and the Normal Distribution Continued

Section 8.2

Z-Scores• A z-score is used to measure how many

standard deviations you are above or below the mean.

• Example) The mean is 50% and the standard deviation is 10%. What is the z-score of 60%?

• What is the z-score of 40%?

• How about the z-score of 65%?

Calculating Z-scores• To calculate your z-score, simply subtract the

mean and divide by the deviation:

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z =x −μ

σ

Eg) The class mean is 50%, the standard deviation is 10% and your mark is 70%. What is your z-score?

More z-scores

The mean is 50%, the deviation is 10%1. What is the z-score of a mark of 45%?

2. What is the z-score of a mark of 83%

3. What percentage of the data has a z-score of less than 2?

What if the numbers don’t work out so well?

Eg) The mean male height is 170 cm with a deviation of 15 cm. a) What is the z-score of a person who is 181 cm tall?

b) What percentile is this person in?

Practice Problems: Height continued

c) What percentile is a person with a height of 153 cm?

d) What percentage of people are between 153 and 181 cm?

e) What percentage of people are taller than 153 cm?

….continued

f) How tall is a person who is in the 92nd percentile for height?

g) In the United States, the Food and Drug Administration recommends human growth hormone for people who are more than 2.25 deviations below the mean for height. At what height are you recommended to take the hormone?

Practice

• Pg. 430 1, 2, 3, 4, 6, 7 Challenge: 11, 12