Download Holt McDougal Algebra 2 - Effingham County Schools

Fitting
Fittingtotoa aNormal
NormalDistribution
Distribution
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
Algebra 2Algebra 2
Holt
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
Objectives
Use tables to estimate areas under
normal curves. Recognize data sets
that are not normal.
Vocabulary
standard normal value
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
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.
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
Example 3: Continued
Z
-2
-1
0
1
2
Holt McDougal Algebra 2
Area
Below
z
X
Values Below
z
Proj.
Act.
Fitting to a Normal Distribution
Example 3: Continued
Z
Area
Below
z
-2
-1
0.02
0.16
0
3
0
1
2
0.5
0.84
0.98
10
17
20
Holt McDougal Algebra 2
X
Values Below
z
Proj.
Act.
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
Holt McDougal Algebra 2