STAT 2035 4.4 & 4.5

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Statistical Sciences
Statistical Sciences 2035
Steve Kopp

Example 4.10 Solution X= # of spoiled milk cartons out of 250 P= P(success)=P(carton being spoiled)=0.01 X~Bin(n=250; p=0.01) We wish to calculate: P(x>5)=1- P(x<=5)=1-[p(0)+P(1)+P(2)+P(3)+P(4)+P(5)] Where P(5)=( 250)(0.01) (0.99) 245 5 Check Np=250(0.01)=2.5 since this is less than 5, we can use the poissom distribution to approx. the p(x>5) with U=np+2.5 −2.5 𝑥 P(x) =(𝑒 2.5 )/𝑥! Thus P(x>5) =1-P(x<5) =10.89% Section4.5 This happen when you sample without replacement and you have a small population. You can use the hypergeomentric distribution For example: N=100 n=15 X=# of defectives out of n=15 nd st P 2 : conditioned on fact that 1 item was defective. P 3 : given 1 2 items were defective We should not us Binomial distribution. (put chosen sample back in the box) Hypergeometric Distribution: 1. to use the HD, you MUST know N 2. it is known that r of them are of a certain kind and N-r of them are of another kind 3. KEY We take a random sample of n items, drawn without replacement, BUT p = P(success) is not the same from trial ( ) 𝑒 𝑒 𝑥 𝑒 𝑒 𝑒 − −𝑥 𝑒
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