Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
A) 0.0378
B) 0.0500
C) 0.1251
D) 0.5000

Question

Quizplus · Accepted Answer

Since 20 cars arrive per 10 minutes, the arrival rate is 2 cars per minute during rush hour. The number of arrivals in a five-minute interval follows a Poisson distribution with a mean of $\lambda = (2	ext{ cars/minute})(5	ext{ minutes}) = 10	ext{ cars}$.
The probability of exactly 5 cars arriving in this interval is:
$P(X=5) = \dfrac{e^{-10}10^5}{5!} \approx 0.0378$
Therefore, the answer is choice A.

Cars Arrive Randomly at a Tollbooth at a Rate of 20