On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next five minute interval is ___.
A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.3610

Question

Quizplus · Accepted Answer

To use the Poisson distribution, we need to know the average rate of cars arriving, which can be calculated by converting the given rate of 6 cars per 15 minutes to a rate per 5 minutes:

6 cars / 15 minutes = 0.4 cars per minute
0.4 cars per minute * 5 minutes = 2 cars in 5 minutes

So the average rate of cars arriving is 2 cars in a 5 minute interval. Now we can use the Poisson distribution formula to calculate the probability of 5 cars arriving:

P(X = 5) = (e^(-2) * 2^5) / 5!
P(X = 5) = 0.0361

Therefore, the probability that five cars will arrive during the next five minute interval is 0.0361. The best choice is (B).

On Saturdays, Cars Arrive at Sami Schmitt's Scrub and Shine