The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsightly blemishes often appear because of improper mixture or other problems. A worker counted the number of blemishes on each door. Most doors had no blemishes; a few had one; a very few had two; and so on. The average number was 0.5 per door. The distribution of blemishes followed the Poisson distribution. Out of 10,000 doors painted, about how many would have no blemishes?
A) About 6,065
B) About 3,935
C) About 5,000
D) About 500

Question

Quizplus · Accepted Answer

The Poisson distribution with an average (λ) of 0.5 can be used to find the probability of 0 blemishes (k=0) using the formula P(X=k) = (e^(-λ) * λ^k) / k!. For k=0, this simplifies to e^(-0.5), which is approximately 0.6065. Therefore, out of 10,000 doors, about 6,065 would have no blemishes.

The Production Department Has Installed a New Spray Machine to Paint