Solution Found!
Compare the Poisson approximation with the correct
Chapter 4, Problem 58P(choose chapter or problem)
Problem 58P
Compare the Poisson approximation with the correct binomial probability for the following cases:
(a) P{X = 2} when n = 8, p = .1;
(b) P{X = 9} when n = 10, p = .95;
(c) P{X = 0} when n = 10, p = .1;
(d) P{X = 4} when n = 9, p = .2.
Questions & Answers
QUESTION:
Problem 58P
Compare the Poisson approximation with the correct binomial probability for the following cases:
(a) P{X = 2} when n = 8, p = .1;
(b) P{X = 9} when n = 10, p = .95;
(c) P{X = 0} when n = 10, p = .1;
(d) P{X = 4} when n = 9, p = .2.
ANSWER:
Solution:
Step 1 of 5:
Let X follows the Binomial distribution with the probability mass function.
P(X = x) = , x = 0, 1, 2,...,n.
Let X follows the Poisson distribution with the probability mass function
P(X = x) =
The claim is to compare the Poisson approximation with the correct Binomial probability