The probability that a rental car will be stolen is 0.0004. If 3500 cars are rented, what is the approximate Poisson probability that 2 or fewer will be stolen?
A).3452
B).2417
C).5918
D).8335

Question

Quizplus · Accepted Answer

The Poisson probability formula is $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the average rate (mean) of occurrence and $k$ is the number of occurrences. Here, $\lambda = 3500 \times 0.0004 = 1.4$. To find the probability of 2 or fewer cars being stolen, we calculate the sum of probabilities for 0, 1, and 2 cars being stolen using the Poisson formula and sum them up. The calculation yields approximately 0.835, or 83.35% when converted to a percentage, which corresponds to choice D.

The Probability That a Rental Car Will Be Stolen Is