holt mcdougal algebra 2 fitting to a normal distribution holt algebra 2 warm up warm up lesson...

Holt McDougal Algebra 2

Fitting to a Normal Distribution Fitting to a Normal Distribution

Holt Algebra 2

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Algebra 2

Holt McDougal Algebra 2

Fitting to a Normal Distribution

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}.

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Use tables to estimate areas under normal curves. Recognize data sets that are not normal.

Objectives

standard normal value

Vocabulary

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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.

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Example 1 : Continued

Holt McDougal Algebra 2

Fitting to a Normal Distribution

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?

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Example 2: Using Standard Normal Values

A. Estimate the probability that a randomly selected student scored less than 148.

Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12.

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Example 2: Continued

B. Estimate the probability that a randomly selected student scored between 154 and 184.

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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.

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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?

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Z AreaBelow

z

X Values Below z

Proj. Act.

-2

-1

0

1

2

Example 3: Continued

Holt McDougal Algebra 2

Fitting to a Normal Distribution

Z AreaBelow

z

X Values Below z

Proj. Act.

-2 0.02 0

-1 0.16 3

0 0.5 10

1 0.84 17

2 0.98 20

Example 3: Continued

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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?

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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.

Holt McDougal Algebra 2

Fitting to a Normal Distribution 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?

Holt McDougal Algebra 2

Fitting to a Normal Distribution Lesson Quiz: Part III