MATH 101 HOMEWORK 10
Due on Wednesday, November 26
Covers sections 7.8, 7.9. For full credit, show all work.
1. A credit card company determines that the waiting time for a customer’s call to be answered by a representative is modelled by an exponential density function with expectation
5 minutes.
(a) (5 marks) What is the probability that a call is answered during the first 2 minutes?
During the first 5 minutes?
(b) (5 marks) The company wants to make sure that 95% of the calls are answered within
the first 10 minutes. Does it have to improve its service? If the average time is still to be
modelled by an exponential density, what expectation should the company aim for?
2. Solve the differential equations:
(a) (5 marks) y 0 + y tan x = 2 cos2 x,
(b) (5 marks) y 0 + 2xy = e−x , y(0) = −1.
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PRACTICE PROBLEMS IN PROBABILITY THEORY
1. A casino slot machine is designed so that the probability of winning x dollars is given
by the exponential density ke−kt , where k can be adjusted by the owner of the machine.
(a) If it costs $1 to play, how should the owner set the value of k so that the average
expected profit is at least 25 cents per customer?
(b) Assume that the owner has set k = 2. What is the probability of winning at least 10
dollars? What is the probability of winning $100 or more?
2. A pizza delivery company determines that the length of time from receiving the order
to delivery is modelled by a normal distribution with expectation 30 minutes and standard
deviation 5 minutes.
(a) What is the probability that the pizza is delivered in less than 35 minutes?
(b) The company wants to advertise that if the pizza is not delivered within x minutes,
it’s free. But it does not want to give away free pizza to more than 1% of its customers.
What should x be?
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