Chapter Eight Day Two

Binomial DistributionsMean and Standard Deviation

Homework

p. 523 14,16,18

p. 529 20,22,24

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)

Make a Histogram of x~B(5,.25)

µx =

σx =

Find the Mean and standard deviation

Form the Binomial CDF.

Binomial Cumulative Distribution Function

x 0 1 2 3 4 5

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)

Example

Normal Approximation to the Binomial

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))

Normal Approximation to Binomial

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

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