1. Fitting to a Normal Distribution
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 2
Holt Algebra 2

2. Find the mean and standard deviation of each data set.
Warm Up
Find the mean and standard deviation
of each data set.
1. {2, 10, 5, 3}
2. {30, 30, 60}
3. {2, 2, 2, 2,2}
4. Determine which data set has the greater standard deviation without calculating it. Explain.
Set A: {73, 120, 54, 81, 66}
Set B: {83, 95, 106, 99, 82}.

3. Objectives Vocabulary
Use tables to estimate areas under normal curves. Recognize data sets that are not normal.
Vocabulary
standard normal value

5. Example 1: Finding Joint and Marginal Relative Frequencies
Jamie can drive her car an average of 432 gallons per tank of gas, with a standard deviation of 36 miles. Use the graph to estimate the probability that Jamie will be able to drive more than 450 miles on her next tank of gas.

6. Example 1 : Continued

7. Check It Out! Example 1
estimate the probability that Jamie will be able to drive less than 400 miles on her next tank of gas?

8. Example 2: Using Standard Normal Values
Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12.
A. Estimate the probability that a randomly selected student scored less than 148.

9. Example 2: Continued
B. Estimate the probability that a randomly selected student scored between 154 and 184.

10. Check It Out! Example 2
Scores on a test are normally distributed with a mean of 142 and a standard deviation of 18. Estimate the probability of scoring above 106.

11. Example 3: Determining Whether Data May Be Normally Distributed
The lengths of the 20 snakes at a zoo, in inches, are shown in the table. The mean is 34.1 inches and the standard deviation is 10.5 inches. Does the data appear to be normally distributed?

12. Example 3: Continued Z
Area
Below z X
Values Below z
Proj.
Act. -2 -1 1 2

13. Example 3: Continued Z
Area
Below z X
Values Below z
Proj.
Act. -2
0.02 -1
0.16 3
0.5 10 1
0.84 17 2
0.98 20

14. Check It Out! Example 3
A random sample of salaries at a company is shown. If the mean is $37,000 and the standard deviation is $16,000, does the data appear to be normally distributed?

15. Lesson Quiz: Part I
Scores on a test are normally distributed with a mean of 200 and a standard deviation of 12. Find each probability.
1. A randomly selected student scored less than 218.
2. A randomly selected student scored between
182 and 200.
3. A randomly selected student scored between 182 and 188.

16. Lesson Quiz: Part II
4. A randomly selected student scored above 224.
5. The weights, in grams, of 30 randomly chosen apples from a large bin are shown below. The mean weight is 110 grams and the standard deviation is 5.5 grams. Does the data appear to be normally distributed?

17. Lesson Quiz: Part III