Participants in a 2 day biking event, cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that at least 2 minutes will elapse between bike riders is closest to _____________.
A).0000
B).0498
C).2635
D).1353
E).4647

Question

Quizplus · Accepted Answer

The probability that at least 2 minutes will elapse between bike riders can be calculated using the Poisson distribution formula, given the average rate of occurrence. With 10 riders crossing the finish line every 15 minutes, the rate is 10 riders per 15 minutes, or 2/3 rider per minute. The probability of no riders in 2 minutes is e^(-4/3), and the probability of exactly one rider in 2 minutes is (4/3)*e^(-4/3). The probability of at least 2 minutes elapsing between riders is 1 minus these probabilities, which is approximately 0.2635.

Participants in a 2 Day Biking Event, Cross the Finish