Question 1

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________
A)0.05
B)0.75
C)0.25
D)0.27
E)0.73

Accepted Answer

The answer of Inquiries arrive at a record message device...

Question 2

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).1353e).4647

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).

Question 3

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

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.

Quiz 6: Continuous Distributions

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________

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 _____________.

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 _____________.