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A lot of N = 100 industrial products contains
Chapter 3, Problem 213SE(choose chapter or problem)
Problem 213SE
A lot of N = 100 industrial products contains 40defectives. Let Y be the number of defectives in a random sample of size 20. Find p(10) by using (a) the hypergeometric probability distribution and (b) the binomial probability distribution. Is N large enough that the value for p(10) obtained from the binomial distribution is a good approximation to that obtained using the hypergeometric distribution?
Questions & Answers
QUESTION:
Problem 213SE
A lot of N = 100 industrial products contains 40defectives. Let Y be the number of defectives in a random sample of size 20. Find p(10) by using (a) the hypergeometric probability distribution and (b) the binomial probability distribution. Is N large enough that the value for p(10) obtained from the binomial distribution is a good approximation to that obtained using the hypergeometric distribution?
ANSWER:
Solution
Step 1 of 2
a) We have find p(10) by using hyper geometric distribution
The pmf of hyper geometric distribution is
Given that the lot size (N)=100
The sample size (n)=20
No.of defectives (r )=40
Now P(10)
=0.1192
Hence by using hyper geometric distribution p(10)=0.1192