Question

Exponential/Poisson

Megacity Bank operates a drive-up teller window that allows customers to complete bank transactions without having to get out of their car. Megacity Bank waiting line times follow an exponential distribution with a service rate of 36 customers per hour.

A.What is the probability that the time to service is 1 minute or less? (show your formula with the numbers plugged in, as well as the answer. You may use the e^(-λ) table, an advanced calculator or excel to get the answer.)

B.What is the probability that the time to service is 2 minutes or less? (again – formulas with numbers plugged in should be included with your answer to show your work.)

C.What is the probability that the time to service is more than 2 minutes (formulas with numbers plugged in should be shown as well as the answer.)

D.What is the probability that exactly 5 customers show up in 5 minutes?

E.What is the probability that at least one customer shows up in 5 minutes?

Answer 1

Answer:

Given,

Service Rate = 0.6 customers per minute

Hence, Mean Time to Service =

Solution-A:

Let the time to service is denoted by variable that has exponential distribution

Probability that time to service is 1 minute or less:

Solution-B:

Probability that time to service is 2 minute or less:

Solution-C:

Probability that time to service time is more than 2 minutes =

Solution-D:

on average there will be 0.6*5=3 customes in 5 minutes

P(x=5)=e^-3*(3^5/5!)=0.1008

Solution-E:

P(x >= 1) = 1 - P(x = 0 ; 3) = 1 - e^-3 = 1 - 0.0498 = 0.9502