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Alg2 Notes 8.7 upload.notebook
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April 16, 2015
warmup
87 Fitting to a Normal Distribution
Warmup ans.
Warmup Answers
Alg2 Notes 8.7 upload.notebook
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April 16, 2015
warmup
Skills we've learned
8.1 Measures of Central Tendency mean, median, mode, variance, standard deviation, expected
value, boxandwhisker plot, interquartile range, outlier8.2 Data Gathering
population, census, sample, random sample, convenience samples, and selfselected samples, underrepresented, overrepresented, bias samples, statistic, parameter8.3 Surveys, Experiments, & Observational Studies
experiment, observational study, controlled experiment, treatment group, control group, randomized comparative experiment8.4 Significance of Experimental Results
hypothesis testing, null hypothesis, zTest, 95% confidence level: If , then you can reject the null hypothesis with 95% certainty. If , then you do not have enough evidence to reject the null hypothesis.
8.5 Sampling Distributions simple random sample, systematic sample, stratified
sample, cluster sample, convenience sample, selfselected sample, probability sample, margin of error8.6 Binomial Distributions
binomial theorem, binomial expansionOh by the way...
1 standard deviation: 68.2%2 standard deviations: 95.4%3 standard deviatons: 99.7%
Learning Target
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.
Alg2 Notes 8.7 upload.notebook
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April 16, 2015
Area Overview
I. Overview of a Normal Curve Area
The area under the normal curve is 1The maximum value of the curve is the meanThe shaded area corresponds to the probability that x is between those values.
The table
interpret z = 1.0
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Standard Normal Value
A Standard Normal Value
Normal Distribution Table
Demonstrating the Standard Normal Curve
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Prob. by Est. Area
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.
The area under the normal curve is always equal to 1. There are 100 squares under the curve. 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 31/100 = 0.31 that she will be able to drive more than 450 miles on her next tank of gas.
There are about 100 squares under the graph
You try
2. Estimate the probability that Jamie will be able to drive less than 400 miles on her next tank of gas.
There are about 19 squares under curve less than 400, so the probability is about 19/100 = 0.19 that she will be able to drive less than 400 miles on the next tank of gas.
There are about 100 squares under the graph
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April 16, 2015
Standard Normal Value
A Standard Normal Value
Prob. by Normal Curve
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.
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April 16, 2015
Cont
Continued...
B. Estimate the probability that a randomly selected student scored between 154 and 184.
3. Scores on a test are normally distributed with a mean of 160 and a standard deviation of 12.
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.
Recogn. Normal Data
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.
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April 16, 2015
You try
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?
No, the data does not appear to be normally distributed. 14 out of 18 values fall below the mean.
Homework
8.7 p.599 #2 16, 21, 22
