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 less than 10 minutes will elapse between car arrivals is _____________.
A).0001
B).9987
C).0013
D).6667
E).1667

Question

Quizplus · Accepted Answer

Given the rate of 10 bike riders per fifteen minutes, we can calculate the probability of an event happening in a shorter interval using the Poisson distribution. The average rate (λ) of bike riders crossing the finish line per minute is 10 riders / 15 minutes = 2/3 riders per minute. For less than 10 minutes between arrivals, we're interested in the probability of at least one arrival in a 10-minute window. The probability of exactly zero events in a given interval in a Poisson process is given by P(0) = e^(-λt), where λ is the average rate and t is the time interval. Here, λ = 2/3 and t = 10, so λt = 20/3. Thus, P(0) = e^(-20/3). The probability of at least one arrival is 1 - P(0), which is 1 - e^(-20/3). This calculation results in a value close to 0.9987, indicating a very high probability of less than 10 minutes elapsing between bike rider arrivals.

Participants in a 2 Day Biking Event, Cross the Finish