The hypergeometric model is used to describe the numbers of elements in differen

Question

The hypergeometric model is used to describe the numbers of elements in different categories observed when drawing a random sample without replacement from a finite population. If there are A elements in one category and B elements in another, for a population of N = A + B, then the probability that a elements from the first category will be observed in a sample of size n is Pr(Xa = a) = A hardware store is purchasing shovels from a new supplier, whose product quality is unknown. The store manager decides to randomly sample n = 5 shovels from a randomly selected carton of N = 24; if he finds 3 or more defective, he will reject the shipment of shovels. Unknown to the manager, the carton contains A = 6 defective shovels and B = 18 nondefectives. Build a table and barchart showing the hypergeometric probabilities for Xa = 0,1, ,5 in a sample of size n = 5 with A = 6 and B = 18. You will find the R functions seq, dhyper. and barplot useful.

Explanation / Answer

Hi again, A =6, B = 18, N =24, n = 5 Let x = 0, 1, ..., 5. I answered part b) and didn't realize there's a part a). P(X = 0) = 0.2016 P(X = 1) = 04320 P(X = 2) = 0.2880 P(X = 3) = 0.0702 P(X = 4) = 0.0064 P(X = 5) = 0.0001 To see the formulas, look at your part b. I detailed theformula and numbers. Hope this helps, Mike

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