# Multiple Choice Questions Probability -Expected Value by lff30040

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```									                Multiple Choice Questions
Probability - Expected Value

1. Cans of soft drinks cost \$0.30 in a certain vending machine. What is the
expected value and variance of daily revenue (Y) from the machine, if X,
the number of cans sold per day has E(X) = 125, and V ar(X) = 50 ?
(a) E(Y ) = 37.5 , V ar(Y ) = 50
(b) E(Y ) = 37.5 , V ar(Y ) = 4.5
(c) E(Y ) = 37.5 , V ar(Y ) = 15
(d) E(Y ) = 37.5 , V ar(Y ) = 15
(e) E(Y ) = 125 , V ar(Y ) = 4.5
2. A crop insurance company establishes the following loss table based upon
previous claims

percent loss       |       0          25       50       100
probability        |       .90       .05      .02       ????

If they write policy that pays a maximum of \$150/hectare, their expected
loss in \$/hectare is approximately:
(a) 5.2
(b) 7.9
(c) 4.5
(d) 37.5
(e) 25.0
3. A rock concert producer has scheduled an outdoor concert. If it is warm
that day, she expects to make a \$20,000 proﬁt. If it is cool that day, she
expects to make a \$5,000 proﬁt. If it is very cold that day, she expects to
suﬀer a \$12,000 loss. Based upon historical records, the weather oﬃce has
estimated the chances of a warm day to be .60; the chances of a cool day
to be .25. What is the producer’s expected proﬁt?
(a) \$5,000

1
(b) \$13,000
(c) \$15,050
(d) \$13,250
(e) \$11,450
4. A restaurant manager is considering a new location for her restaurant.
The projected annual cash ﬂow for the new location is:

Annual
Cash Flow            \$10,000 \$30,000 \$70,000 \$90,000 \$100,000
Probability             0.10    0.15    0.50    0.15        ?

The expected cash ﬂow for the new location is:
(a) \$12,800
(b) \$64,000
(c) \$70,000
(d) \$60,000
(e) \$50,000
5. An insurance company has estimated the following cost probabilities for
the next year on a particular model of car:

cost          |      \$0     \$500   \$1000     \$2000
prob          |     .60     .05     .13      ????

The expected cost to the insurance company is (approximately):
(a) \$155
(b) \$595
(c) \$875
(d) \$645
(e) \$495

6. Before planting a crop for the next year, a producer does a risk assess-
ment. According to her assessment, she concludes that there are three
possible net outcomes: a \$7,000 gain, a \$4,000 gain, or a \$10,000 loss with
probabilities 0.55, 0.20 and 0.25 respectively. The expected proﬁt is:
(a) \$3,850
(b) \$0
(c) \$2,150
(d) \$2,500

c 2006 Carl James Schwarz                 2
(e) \$800
7. A business evaluates a proposed venture as follows. It stands to make a
proﬁt of \$10,000 with probability 3/20, to make a proﬁt of \$5,000 with
probability 9/20, to break even with probability 1/4 and to lose \$5,000
with probability 3/20. The expected proﬁt in dollars is:
(a) 1,500
(b) 0
(c) 3,000
(d) 3,250
(e) - 1,500
8. The average length of stay in a hospital is useful for planning purposes.
Suppose that the following is the distribution of the length of stay in a
hospital after a minor operation:

Days           2     3         4       5       6
Prob         .05   .20       .40     .20       ?

The average length of stay is:
(a) .15
(b) .17
(c) 3.3
(d) 4.0
(e) 4.2
9. An insurance company issues a policy on a small boat under the following
conditions: The replacement cost (\$5000) will be paid for a total loss. If
it is not a total loss, but the damage is more than \$2000, then \$1500 will
be paid. Nothing will be paid for damage costing \$2000 or less and of
course nothing is paid out if there is no damage. The company estimates
the probability of the ﬁrst three events as .02, .10, and .30 respectively.
The amount the company should charge if it wishes to make a proﬁt of
\$50 above the expected amount paid out in a year is:
(a) \$250
(b) \$201
(c) \$300
(d) \$1200
(e) \$165

c 2006 Carl James Schwarz               3

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