1. Normal Distributions and Z-Scores
Accelerated Math 3

2. Normal Distributions
Last year we learned about normal distributions and the Empirical Rule.

3. Normal Distributions
The Empirical Rule tells us the probability that a certain range of data falls within one, two, or three standard deviations of the mean.
is the mean and is the standard deviation of the data set.

4. Ex. 1: Word Problem
The data for the SAT is normally distributed with a mean of 1000 and standard deviation What is the probability that a randomly selected student scored between a 640 and 1180?

5. Normal Distributions and Z-Scores
What happens when a value doesn’t quite fit in exactly one, two or three standard deviations?
We can use z-scores and z-tables!
Z-scores tell us exactly how many standard deviations away a value is from the mean and the z-table gives us the probability a value is below that amount.

6. Z-Scores
We can find Z-Scores by using the formula:

7. Example 2:
Looking back at our SAT example, lets find the probability that a student scores under 1200.

8. Example 3:
What if I wanted to know the percent of test takers who score above a 1200?

9. Example 4:
What if I wanted to know the z-score for a score between 900 and 1300?

10. Ex 5: Working Backwards
You run a Tootsie Pop factory and want to make a guarantee that your Tootsie Pops will last a certain number of licks. If your mean is 964 licks with a standard deviation of 51 licks, how many licks should you guarantee your Tootsie Pops will last so that 90% last that long?