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

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        (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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