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 _____________.
A) .0000
B) .0498
C) .2635
D) .1353
E) .4647

Question

Quizplus · Accepted Answer

We can use Poisson distribution to model the arrival of bikers at the finish line. Let λ be the expected number of bikers finishing per 15 minute interval. Then λ = 10.

To find the probability that at least 2 minutes will elapse between bike riders, we can find the probability that no bike riders finish in a 2 minute interval. Let X be the number of bikers that finish in a 2 minute interval. Then X has a Poisson distribution with mean μ = 10*(2/15) = 4/3.

P(X = 0) = e^(-μ)μ^0/0! = e^(-4/3) ≈ 0.2635

Therefore, the answer is (C).

Participants in a 2 Day Biking Event,cross the Finish Line