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?
Service Rate = 0.6 customers per minute
Hence, Mean Time to Service =
Let the time to service is denoted by variable that has exponential distribution
Probability that time to service is 1 minute or less:
Probability that time to service is 2 minute or less:
Probability that time to service time is more than 2 minutes =
on average there will be 0.6*5=3 customes in 5 minutes
P(x >= 1) = 1 - P(x = 0 ; 3) = 1 - e-3 = 1 - 0.0498 = 0.9502
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