Math 218 (Fall 2008) Quiz 6 Solutions TA: Wei Lin
Name: Section (circle one): 2pm 3pm 4pm
1. (6 pts) Customer arrivals at a bank teller’s window follow a Poisson distribution with a
mean rate of 2 customers per 10 minutes.
(a) Find the probability that there will be 2 or more customers arriving between 9:30am
and 9:45am.
Solution. Let Xbe the number of customers arriving between 9:30am and 9:45am.
Then Xis Poisson with µ= (2/10)15 = 3, and P(X≥2) = 1 −P(X= 0) −P(X=
1) = 1 −e−3−e−33≈.8009.
(b) A clerk’s working hours are from 9:00am to noon. Find the expected number and
standard deviation of the number of customers arriving during her working hours
on a particular day.
Solution. Let Xthe number of customers arriving between 9:00am and noon. Then
EX= (2/10)180 = 36 (customers) and σX=√36 = 6 (customers).
(c) Since there is no customer waiting at the window, the clerk decides to leave 20
minutes for a break. Find the probability that the next customer will arrive before
she is back.
Solution. We just need to find the probability that at least one customer will arrive
in 20 minutes. Let Xbe the number of customers arriving in 20 minutes. Then Xis
Poisson with µ= (2/10)20 = 4, and P(X≥1) = 1 −P(X= 0) = 1 −e−4≈.9817.
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