MCE 4532

BASC CHARACTERSTCS It models that the total number of successes in a size sample drawn without replacement from a finite population.In the population, k items can be classified as successes, and N - k items can be classified as failures. It differs from the binomial only in that the population is finite and the sampling from the population is without replacement & probability of success be constant on every trialTrials are dependent

n= sample size N=population size k=successes in population x=number of successes in sample h(x; N, n, k) = [ kCx ] [ N-kCn-x ] / [ NCn ]

The hyper-geometric distribution has the following properties:

The mean of the distribution is equal to:n * k / N .

The variance is:n * k * ( N - k ) * ( N - n ) / [ N2 * ( N - 1 ) ]

APPROXMATONSBinomial Approximation Requariments :If A+B=N and n 0.05N , Binomial can be used instead of hypergeometric distributionPoisson Approximation Requariments: Poisson can be used instead of hypergeometric distribution

Example :A carton contains 24 light bulbs, three of which are defective. What is the probability that, if a sample of six is chosen at random from the carton of bulbs, x will be defective? What is the probability that no bulbs will be defective??

What is the probability that 3 bulbs will be defective??

Example:Suppose that a shipment contains 5 defective items and 10 non defective items .If 7 items are selected at random without replacement , what is the probability that at least 3 defective items will be obtained? N=15 (5 defective , 10 nondefective ) n=7