Let the Random Variable X Denote the Number of Defective $n \leq .05 \mathrm {~N}$

Let the random variable X denote the number of defective items in the lot, A denote the event that the lot is accepted, and p denote the proportion of defective items in the lot. Which of the following statements is not true?

A) If the sample size n is large relative to the lot size N, then the probability of accepting the lot, P(A) , is calculated using the hypergeometric distribution.
B) When the sample size n is small relative to the lot size N (the rule of thumb suggested in your text was $n \leq .05 \mathrm {~N}$
) , then the probability of accepting the , P(A) , is calculated using the binomial distribution.
C) If the probability of accepting the lot, P(A) , is large only when p is small (this, of course, depends on the specified critical value c) , then the Poisson approximation to the binomial distribution is justified.
D) The larger value of p, the larger the probability P(A) of accepting the lot.
E) All of the above statements are true.