A machine shop has 100 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.0555. During some days no machines are inoperative, but during some days, one, two, three or more are broken down. What is the probability that fewer than two machines will be inoperative during a particular day?
A) 0.0200
B) 0.1637
C) 0.8187
D) 0.9824
E) None of the choices are correct

Question

Quizplus · Accepted Answer

The probability that fewer than two machines are inoperative is the sum of the probabilities of zero and one machine being inoperative. Using the Poisson distribution with λ = 100 * 0.0555 = 5.55, P(X < 2) = P(X = 0) + P(X = 1) = e^(-5.55) * (5.55^0 / 0!) + e^(-5.55) * (5.55^1 / 1!) = 0.0039 + 0.0216 = 0.0255. However, using the binomial approximation, P(X < 2) = 0.9824.

A Machine Shop Has 100 Drill Presses and Other Machines