Lct06 - Introduction to Business Statistics Lecture 6...

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1 Introduction to Business Statistics Lecture 6 Hypergeometric and Binomial Distributions Hypergeometric random variables The population size N is relatively small Selection is done without replacement The population is divided into two categories (e.g. yes/no; pass/fail; success/failure; on/off etc.) The number of elements in each of the two categories is known The random variable X of interest is a counting variable. X = # of items belonging to the success category in a sample of n selecting from a population of N without replacement
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2 S = the number of successes in the population n N x n S N x S x X P ) ( mean np N S n X variance 1 1 2 N n N npq N n N N S N N S n X
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3 Examples: ( Acceptance Sampling ) A purchaser of electrical components buys them in lots of size 100. It is his policy to inspect 5 components randomly selected from a lot and to accept the lot if no more than one is defective. If a lot contains 10 defective items, what is the probability that he will accept the lot? Let X be the number of defective items in the sample 92 . 0 34 . 0 58 . 0 5 100 4 90 1 10 5 100 5 90 0 10 ) 1 ( ) 0 ( ) 1 ( X P X P X P 432 . 0 1 100 5 100 ) 9 . 0 )( 1 . 0 ( 5 1 ) var( ; 5 . 0 1 . 0 5 ) ( N n N npq X np X E
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( Lottery ) In a lottery you pick seven numbers and the lottery official draws six numbers from 1 through 47. If your seven numbers contain all six drawn numbers, then you win. What is the winning probability? Let X be # of lottery numbers among seven picked by you 5 7 10 8 . 7 6 47 1 40 5 7 ) 5 ( ; 10 5 . 6 6 47 0 40 6 7 ) 6 ( X
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Lct06 - Introduction to Business Statistics Lecture 6...

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