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Problems 331be installed elsewhere. Estimate the optimistic
life, most likely life, and pessimistic life for tele-
phone poles. What percentage of all telephone
poles would you expect to have a total useful life
greater than your estimated optimistic life?
10-2 The purchase of a used pickup for $9000 is being con-
sidered. Records for other vehicles show that costs for
oil, tires, and repairs about equal the cost for fuel. Fuel
costs are $990 per year if the truck is driven 10,000
miles. The salvage value after 5 years of use drops
about $0.08 per mile. Find the equivalent uniform
annual cost, if the interest rate is 8%. How much
does this change if the annual mileage is 15,000?
5000?
10-3 A heat exchanger is being installed as part of a plant
modernization program. It costs $80,000, including
installation, and is expected to reduce the overall plant
fuel cost by $20,000 per year. Estimates of the use-
fullife of the heat exchanger range from an optimistic
12 years to a pessimistic 4 years. The most likely value
is 5 years. Using the range of estimates to compute
the mean life, determine the estimated before-tax rate
of return. Assume the heat exchanger has no salvage
value at the end of its useful life.
10-4 For the data in Problem 10-2 assume that the 5000,
10,000, and 15,000 mileage values are, respectively,
pessimistic, most likely, and optimistic estimates. Use
a weighted estimate to calculate the equivalent annual
cost.
10-5 When a pair of dice are tossed, the results may be
any whole number from 2 through 12. In the game of
craps one can win by tossing either a 7 or an lion the
first roll. What is the probability of doing this?(Hint:
There are 36 ways that a pair of six-sided dice can be
tossed. What portion of them result in either a 7 or an
II?) (Answer:8/36)
10-6 Annual savings due to an energy efficiency project
have a most likely value of $30,000. The high esti-
mate of $40,000 has a probability of 0.2, and the low
estimate of $20,000 has a probability of 0.30. What
is the expected value for the annual savings?
(Answer: $29,000)
10-7 Over the last 10 years, the hurdle or discount rate for
projects from the firm's research and development
division been 10% twice, 15% three times, and 20%
the rest of the time. There is no recognizable pat-
tern. Calculate the probability distribution and the
expected value for next year's discount rate.10-8 The construction time for a bridge depends on weather
conditions. The project is expected to take 250 days
if the weather is dry and the temperature is hot. If
the weather is damp and cool, the project is expected
to take 350 days. Otherwise, it is expected to take
300 days. Historical data suggest that the probability
of cool, damp weather is 30% and that of dry, hot
weather is 20%. Find the project's probability distri-
bution and expected completion time.
10-9 You recently had an auto accident that was your fault.
If you have another accident or receive a another mov-
ing violation within the next 3 years, you will become
part of the "assigned risk" pool, and you will pay an
extra $600 per year for insurance. If the probability
of an accident or moving violation is 20% per year,
what is the probability distribution of your "extra"
insurance payments over the next 4 years? Assume
that insurance is purchased annually and that viola-
tions register at the end of the year-just in time to
affect next year's insurance premium.
10-10 Two instructors announced that they "grade on the
curve," that is, give a fixed percentage of each of the
various letter grades to each of their classes. Their
curves are as follows:Grade
A
B
C
D
FInstructor A
10%
15
45
15
15Instructor B
15%
15
30
20
20If a random student came to you and said that his
object was to enroll in the class in which he could ex-
pect the higher grade point average, which instructor
would you recommend? (Answer: GPAB =. 1.95,
InstructorA)
10-11 A man wants to determine whether or not to invest
$1000 in a friend's speculative venture. He will do so
if he thinks he can get his money back in one year.
He believes the probabilities of the various outcomes
at the end of one year are as follows:Result
$2000 (double his money)
1500
1000
500
o (lose everything)Probability
0.3
0.1
0.2
0.3
0.1--
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