1. 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?
CAN YOU DO THIS?...What percent of the students would have a grade of 70 or higher?

2. 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?

3. 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?
The speed of that car is 1.25 standard deviations ABOVE the mean.
1.25
-1.75
| | | | | | |
(z =)
What is the z-score for a car that is traveling 60mph?
The speed of that car is 1.75 standard deviations BELOW the mean.

4. To find the percentage or probability that a certain interval is possible, we use the z-score table.
The z-score table always tells the percentage (as a decimal) 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)
To get a percentage to the RIGHT of a z-score, you would just subtract the TABLE value from 100%.