Question

A busy restaurant determined that between 6:30 P.M. and 9:00 P.M. on Friday nights, the arrivals of customers are Poisson distributed with an average arrival rate of 4.32 per minute. *(Round your answer to 2 decimal places.) **(Round your answer to 4 decimal places.)

(a) What is the probability that at least 11 minutes will elapse between arrivals?

(b) What is the probability that at least 4 minutes will elapse between arrivals?

(c) What is the probability that at least 1 minute will elapse between arrivals?

(d) What is the expected amount of time between arrivals?

Answer 1

Here, we are given the distribution for arrivals as:

a) The probability here is computed as:

As the average number of arrivals is 4.32 per minute, therefore the average number of arrivals in 11 minutes would be given as: 4.32*11 = 47.52.

Now the probability here is computed as:

Therefore 0 is the approximate probability here.

This is also intuitive because there are 47.52 arrivals expected in 11 minutes, therefore it is highly unexpected that there would be no arrival in 11 minutes.

b) The required probability here is computed as:

c) The required probability here is computed as:

Therefore 0.0133 is the required probability here.

d) The expected amount of time between arrivals is computed as:

= 1/4.32

= 0.2315 minutes.