Compare the Poisson approximation with the correct

Chapter 4, Problem 58P

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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.

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


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