The true proportion of accounts receivable with some kind of error is .02 for Venal Enterprises. If an auditor randomly samples 200 accounts receivable, what is the approximate Poisson probability that fewer than two will contain errors?
A).1038
B).0916
C).1465
D).0015

Question

Quizplus · Accepted Answer

The Poisson probability can be calculated as follows:
λ = np = 200 * 0.02 = 4
P(X < 2) = P(X = 0) + P(X = 1)
= e^(-λ) * λ^0 / 0! + e^(-λ) * λ^1 / 1!
= e^(-4) * 4^0 / 0! + e^(-4) * 4^1 / 1!
≈ 0.0916
Therefore, the approximate Poisson probability that fewer than two accounts receivable will contain errors is 0.0916, which corresponds to answer choice B.

The True Proportion of Accounts Receivable with Some Kind of Error