We claimed that the binomial distribution is a good model for the hypergeometric

Question

We claimed that the binomial distribution is a good model for the hypergeometric distribution, in the right circumstances. Suppose samples of size 50 are being tested. Consider units defective with probability p= 0.06, so that if the size of the population is N, M= N p units are defective. Use R to find the minimum population size N for which no corresponding values in the binomial and hypergeometric PMFs differ by more than 0.01. (In other words, find N for which |P(Xbinom =x) P(Xhyper=x)| 0.01, for all values of x in the sample space.)

Does your answer change if defect probability p is changed?

Explanation / Answer

Below is the R code.

p <- 0.06
size <- 50
exit <- 0
for (N in 50:100) {
m <- round(N*p) # m= N*p
n <- N - m # n = N - N*p
for (x in 0:m) { # x should be between 0 and m
if (abs(dbinom(x,size,p)-dhyper(x,m,n,size)) <= 0.01) {
print(x)
print(m)
print(n)
print("The minimum size is")
print(N)
exit <- 1 # Exit the loop
break
}
}
if (exit == 1) {
break # Exit the loop
}
}

I got the minimum population size of 55.

Yes, on changing the defect probability, the minimum population size changes.

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