a) Find the value of p(10) by using hypergeometric probability

usagirl007A 2021-09-30 Answered
a) Find the value of p(10) by using hypergeometric probability distribution.
b) Find the value of p(10) by using binomial probability distribution.
Determine the value for p(10) obtained from the binomial distribution is a good approximation to that obtained using the hypergeometric distribution when the N large enough.
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davonliefI
Answered 2021-10-01 Author has 79 answers

a) Calculation:
A hypergeometric probability distribution of random variable Y is,
p(y)=(ry)(Nrny)(Nn);y=0,1,2,,n,yr and nyNr
Let Y is defined as the number of defectives in a random sample of size 20. A lot of 100 industrial products contains 40 defectives. That is, r=40,N=100,n=20.
The value of p(10) is,
P(Y=10)=(4010)(100402010)(10020)
=0.11922
Hence, the value of p(10) by using hypergeometric probability distribution is 0.1192.
b) Calculation:
A random variable Y is a binomial distribution based on n trails with success probability p if and only if,
p(y)=(ny);pyqny,y=0,1,2,,n and 0p1
Let Y is defined as the number of defectives. A random sample of size 20 with a lot of 100 industrial products contains 40 defectives. That is, n=20,p=0.4(=40100),
The value of p(10) is,
P(Y=10)=(2010)(0.4)10(0.6)2010
=0.117
Hence, the value of p(10) by using binomial probability distribution is 0.117.
It is clear that the value of p(10) by using binomial approximation and using hypergeometric distribution are almost same this indicates that when N is large the binomial distribution is a good approximation to hypergeometric distribution.

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