1. Z-Scores are measurements of how far from the center (mean) a data value falls.
Ex: A man who stands 71.5 inches tall is 1 standard deviation ABOVE the mean.(z-score = 1)
Ex: A man who stands 64 inches tall is 2 standard deviations BELOW the mean. (z-score = -2)
Adult Male Heights

2. Based upon the Empirical Rule, we know the approximate percentage of data that falls between certain standard deviations on a normal distribution curve.
Example:
If a class of test scores has a mean of 65 and standard deviation of 9, then what percent of the students would have a grade below 56?

3. Standardized Scores (aka z-scores)
Z-score represents the exact number of standard deviations a value, x, is from the mean.
mean
observation (value)
standard deviation
Example: (test score problem)
What would be the z-score for a student that received a 70 on the test?

4. What is the z-score for a car that is traveling 60mph?
Example: The mean speed of vehicles along a particular section of the highway is 67mph with a standard deviation of 4mph. What is the z-score for a car that is traveling at 72 mph?
What is the z-score for a car that is traveling 60mph?
Mark the z-scores on the number line below
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(z =)

5. Z-scores are also called standardized scores. To calculate any z-score:
𝑧= 𝑥 − 𝑥 𝑠
American Adult Males: mean of 69 inches and standard deviation of 2.5 inches.
What is the standardized score for a male with a height of 72 inches?
What is the standardized score for a male with a height of 62 inches?

6. To find the proportion or probability that a certain interval is possible, we use the z-score table.
The z-score table always tells the proportion to the LEFT of that z-score value.
What percentage of the data will have a z-score of less than 1.15? P(z < 1.15)

7. Other Examples:
Find P(z < 0.22)
2) Find P(z > 0.22)
3) Find P(0.22 < z < 1.15)