On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen-minute interval.The probability that at least 2 minutes will elapse between car arrivals is ___.
A)0.0000
B)0.4493
C)0.1353
D)1.0000
E)1.0225

Question

Quizplus · Accepted Answer

The probability that at least 2 minutes will elapse between car arrivals is the complement of the probability that no more than 1 minute will elapse between car arrivals. The probability that no more than 1 minute will elapse between car arrivals is the probability that 0 or 1 car arrives in a 1-minute interval. The probability that 0 cars arrive in a 1-minute interval is e^(-6/15) = 0.8905. The probability that 1 car arrives in a 1-minute interval is (6/15) * e^(-6/15) = 0.1095. Therefore, the probability that no more than 1 car arrives in a 1-minute interval is 0.8905 + 0.1095 = 1.0000. The probability that at least 2 minutes will elapse between car arrivals is 1 - 1.0000 = 0.0000.

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