Binomial Distributions Mean and Standard Deviation.

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Presentation transcript:

Binomial Distributions Mean and Standard Deviation

p ,16,18 p ,22,24

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

 µ x =  σ x =

 Form the Binomial CDF. x P(x)

 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)

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

 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))

 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)

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