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Binomial Distributions Mean and Standard Deviation.

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Presentation on theme: "Binomial Distributions Mean and Standard Deviation."— Presentation transcript:

1 Binomial Distributions Mean and Standard Deviation

2 p. 523 14,16,18 p. 529 20,22,24

3  Make a probability Distribution for X~B(5,.25).  This is called a Binomial PDF x012345 P(x)

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5  µ x =  σ x =

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7  Form the Binomial CDF. x012345 P(x)

8  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)

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10  The Practice of Statistics, Third edition - Content The Practice of Statistics, Third edition - Content

11  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))

12  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)

13 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


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