Question 1
(a)
A particular type of device is manufactured and shipped to stores. Due to problems with
the manufacturing process, some devices do not work. Say we manufacture 20 devices and
ship them to two stores. Store A receives 8 devices and Store B receives 12 devices. Assume
we know that 2 of the 20 devices
do not
work.
(i) Let
X
= the number of working devices received by Store A. What is the probability
distribution of the random variable
X
? You need to specify the name of the distribution,
all necessary parameters, the possible values of
X
.
(ii) Still assuming that 2 of the 20 devices
do not
work, what is the probability that Store
A receives 8 working devices?
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The device in question is made up of 200 individual components. Based on experience
with the manufacturing process, we know that the probability that any particular compo
nent on a device is defective is 0
.
005. Assume mutual indepedence for whether or not the
components on a device are defective.
Say we randomly choose one device to inspect before shipping. Let
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 Spring '08
 Staff
 Normal Distribution, Probability theory, 2 grams, 10,000 dollars, Store B

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