Download Alg2 Notes 8.7.notebook

Alg2 Notes 8.7.notebook
March 20, 2013
8­7 Fitting to a Normal Distribution 3. What is the probability of correctly choosing the winning team of March Madness if picking randomly?
Warm­up Answers
3. What is the probability of correctly choosing the winning team of March Madness if picking randomly?
Alg2 Notes 8.7.notebook
March 20, 2013
8­7 Fitting to a Normal Distribution 1. Use tables to estimate areas under normal curves.
2. Recognize data sets that are not normal. If data is truly normal, we can make observations and hypothesis.
I. Overview of a Normal Curve Area
The area under the normal curve is 1
The maximum value of the curve is the mean
The shaded area corresponds to the probability that x is between those values.
Alg2 Notes 8.7.notebook
March 20, 2013
interpret z = ­1.0
A Standard Normal Value
Alg2 Notes 8.7.notebook
March 20, 2013
Demonstrating the Standard Normal Curve
II. Finding Probability By Estimating Area
1. Jamie can drive her car an average of 432 miles 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.
There are about 100 squares under the graph
The area under the normal curve is always equal to 1. Each square on the grid has an area of 10(0.001) = 0.01. Count the number of grid squares under the curve for values of x greater than 450. There are about 31 squares under the graph, so the probability is about 31(0.01) = 0.31 that she will be able to drive more than 450 miles on her next tank of gas.
Alg2 Notes 8.7.notebook
March 20, 2013
2. Estimate the probability that Jamie will be able to drive less than 400 miles on her next tank of gas. There are about 100 squares under the graph
There are about 19 squares under curve less than 400, so the probability is about 19(0.01) = 0.19 that she will be able to drive less than 400 miles on the next tank of gas.
A Standard Normal Value
Alg2 Notes 8.7.notebook
March 20, 2013
III. Finding Probabilities Using Standard Normal Values
3. 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.
Use the table to find the area under the curve for all values less than ­1, which is 0.16. The probability of scoring less than 148 is about 0.16.
Continued... 3. Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12.
B. Estimate the probability that a randomly selected student scored between 154 and 184.
Area=0.31
Area=0.98
Subtract the areas to eliminate where the regions overlap. The probability of scoring between 154 and 184 is about 0.98 – 0.31 = 0.67.
Alg2 Notes 8.7.notebook
March 20, 2013
IV. Recognizing Normally Distributed Data
4. 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?
No, the data does not appear to be normally distributed. 5. 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?
Z
AreaBelow z X
­2
0.02
­1
0.16
0
0.5
1
0.84
2
0.98
Values Below z
Proj.
Act.
No, the data does not appear to be normally distributed. 14 out of 18 values fall below the mean.
Alg2 Notes 8.7.notebook
8.7 p.599 #2 ­ 16, 21, 22
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March 20, 2013