Investígate how well the binomial approximation to the hypergeometric distributi

Question

Investígate how well the binomial approximation to the hypergeometric distribution works. A rule of thumb given in class is: this approximation works well if n/N does not exceed 0.05. You will compute the value of the hypergeometric pmf for various combinations of x, r, n, and N. Below, x is the value of the hypergeometric random variable X. You may do only 1 of 3, 2 of 3 or all three parts below for a maximum total of ten bonus ponts. Five extra credit points: Compute the hyderegeometric pmf and its binomial approximation for the following combinations: n=20, N= 200, r=50, x=1, 3, 5, 7, 8, 10. n=5, N=100, r=50, x=0, 1, 2, 3, 4, 5. n=20, N = 500, r=0, 1, 2, 3, 4, 5, 7.

Explanation / Answer

(1) For the Population size N=200, sample size n=20, Population success r=50 and given values of X(successes in the sample): 1,3,5,7,8,10, the follwoing Pmf would be generated

Since n/N=20/200= 0.1>0.05, the binomial approximations do not work

Success(X) Hypergeometric Probability Binomial approximations 1 0.0171 - 3 0.131 - 5 0.213 - 7 0.1133 - 8 0.0573 - 10 0.0074 -

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