A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is:
A) larger than $0.95$.
B) larger than $0.50$.
C) between $0.25$ and $0.50$.
D) smaller than 0.05.

Question

A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is: 
A) larger than $0.95$.
B) larger than $0.50$.
C) between $0.25$ and $0.50$.
D) smaller than 0.05.

Quizplus · Accepted Answer

When the probability of success for a binomial distribution is very small (i.e. p < 0.05), even large values of n will result in very few successes. In this case, a Poisson distribution with parameter λ = np is a good approximation for the binomial distribution.

A Binomial Distribution for Which the Number of Trials N 0.950.950.95

A Binomial Distribution for Which the Number of Trials N $0.95$