Question : The probability distribution of a certain overhead cost is f(x) = 2(1x)2, where x is production : 2141834
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
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1) The probability distribution of a certain overhead cost is f(x) = 2(1x)^{2}, where x is production hours per day. Determine the expected value and variance for this distribution if the number of production hours per day ranges from 4 to 11 hours.
2) Gopher Manufacturing is considering purchasing new calibration equipment to improve the quality of its processes. The equipment has an initial cost of $66,000 and a market value of $52,000 at the end of its useful life of 10 years. Net annual revenue is estimated based on the production and market conditions and is shown below. If the optimistic and pessimistic values each have an estimated 11% chance of occurring, determine whether the equipment should be purchased on the basis of the expected value of AW. Use a MARR of 8% per year.

Optimistic 
Most likely 
Pessimistic 
Net annual revenue, $/year 
93,500 
90,000 
88,500 
3) Kewpie, Inc. is considering purchasing a new set of packaging and labeling equipment. A comparison of estimated cash flows is shown below.
Item 
P = 0.2 
P = 0.15 
P = 0.65 
Initial investment, $ 
210,000 
210,000 
210,000 
Net annual revenue, $/year 
265,000 
250,000 
240,000 
Market value, $ 
30,000 
32,000 
37,000 
Project life, years 
5 
5 
5 
If straightline depreciation with a salvage value of $32,000 and a useful life of 5 years is used, determine whether Kewpie should invest in the equipment on the basis of the expected value of aftertax PW. Assume an effective tax rate of 35% and a MARR of 10% per year.
4) An engineer is considering the size of a reservoir for flood control in the northern part of Germany. The size of the reservoir is closely related to the annual rainfall. In addition, there will be reparation costs from damages when the amount of rainfall exceeds the design capacity. If such damage occurs, it is estimated that the annual reparation cost will be 2.3% of the capital investment. The probabilities of specific amounts of rainfall per year and the estimated investment costs of the reservoir are given below. Using an interest rate of 8% per year and a study period of 11 years, determine the appropriate investment on the basis of AW.
Annual Rainfall, M^{3}

Probability of Greater Rainfall 
Estimated Capital Investment, $ 
110 
0.6 
2,500,000 
120 
0.2 
2,550,000 
130 
0.1 
2,600,000 
140 
0.055 
2,650,000 
150 
0.045 
2,700,000 
5) The estimated annual cash flow of an investment project along with associated probabilities are given below. Determine the expected present worth of this annual cash flow series at an interest rate of 11% per year.
Year 
P = 0.5 
P = 0.4 
P = 0.1 
0 
$57,000 
$59,000 
$57,500 
1 
$3100 
$3000 
$3100 
26 
$3250 
$3000 
$3100 
7 
$3400 
$6000 
$3100 
6) Buffalo Manufacturing is considering purchasing new equipment with an initial cost of $65,000 and zero market value at any time of its useful life. The company expects this new equipment to generate additional net revenue of $6700 per year. Due to the harsh environment in which the equipment will be operated, the useful life of the equipment is uncertain. The estimated probabilities of different useful lives are shown below. Calculate the expected present worth and variance of present worth associated with the purchase of the equipment. Assume the company's MARR is 11% per year.
Useful life, Years (N) 
P(N) 
3 
0.1 
4 
0.1 
5 
0.15 
6 
0.18 
7 
0.47 
7) Amy wants to estimate the average number of items per purchase at the express lane of a local grocery store. She has estimated the following probabilities based on a sample size of 50 customers. Determine the expected value, variance, and standard deviation of items per purchase.
Items per Purchase 
Probability 
1 
0.29 
2 
0.16 
3 
0.15 
4 
0.18 
5 
0.22 