Binomial Distributions Mean and Standard Deviation.
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Transcript of Binomial Distributions Mean and Standard Deviation.
![Page 1: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/1.jpg)
Chapter Eight Day Two
Binomial DistributionsMean and Standard Deviation
![Page 2: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/2.jpg)
Homework
p. 523 14,16,18
p. 529 20,22,24
![Page 3: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/3.jpg)
Make a probability Distribution for X~B(5,.25).
This is called a Binomial PDF
Binomial Probability Distribution
x 0 1 2 3 4 5
P(x)
![Page 4: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/4.jpg)
Make a Histogram of x~B(5,.25)
![Page 5: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/5.jpg)
µx =
σx =
Find the Mean and standard deviation
![Page 6: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/6.jpg)
![Page 7: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/7.jpg)
Form the Binomial CDF.
Binomial Cumulative Distribution Function
x 0 1 2 3 4 5
P(x)
![Page 8: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/8.jpg)
Suppose James guesses on each question of a 10 item multiple choice test with four choices for each question.
p(X > = 1)
P(x > 6)
Example
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Normal Approximation to the Binomial
![Page 10: Binomial Distributions Mean and Standard Deviation.](https://reader036.fdocument.org/reader036/viewer/2022082600/5a4d1af27f8b9ab05997f160/html5/thumbnails/10.jpg)
The Practice of Statistics, Third edition - Content
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If x~B(n , p) then
P(x≤ k) = binomialcdf( n,p) Is approximately ~N(np, sqr(npq)) so
P(x ≤ k) ~ normalcdf(lower,k, np, sqr(npq))
Normal Approximation to Binomial
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One way of checking for Undercoverage, Nonresponse, and other sources of error in a sample survey is to compare the sample with known facts about the population. About 12% of American adults are black. The number X of blacks in a random sample of 1500 adults should therefore be X~B(1500, .12)
Example
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What is the mean and standard deviation of X?
Find p( 165≤ x≤ 195) using the binomial formula and by using the Normal approximation to the binomial
Example