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**

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