U-Haul is an American moving equipment and storage rental company, based in Phoe
ID: 3335253 • Letter: U
Question
U-Haul is an American moving equipment and storage rental company, based in Phoenix, Arizona, that has been in operation since 1945. The company estimates the following probability distribution table for their furniture dolly rentals. The rent of a dolly per day is $40. If a customer wants a furniture dolly and none is available, the store gives a $15 coupon.
Demand
Relative Frequency
Revenue
Cost
0
.35
0
0
1
.30
40
0
2
.20
80
0
3
.10
80
15
4
.05
80
30
a. Calculate and interpret the mean and the standard deviation of demand for furniture dollies.
b. Calculate and interpret the mean and the standard deviation of revenue for furniture dollies.
c. Calculate and interpret the mean and the standard deviation of cost for furniture dollies.
d. What is the expected profit from furniture dollies?
Demand
Relative Frequency
Revenue
Cost
0
.35
0
0
1
.30
40
0
2
.20
80
0
3
.10
80
15
4
.05
80
30
Explanation / Answer
(a) Mean of demand for furniture dollies = 0 * 0.35 + 1 * 0.30 + 2 * 0.20 + 3 * 0.10 + 4 * 0.05 = 1.2 dollies
Variance of demand for furniture dollies = 0.35 * (0-1.2)2 + 0.30 * (1 - 1.2)2 + 0.20 * (2-1.2)2 + 0.10 * (3 - 1.2)2 + 0.05 * (4 - 1.2)2 = 1.36
Standard deviation of demand for furniture dollies = sqrt(1.36) = 1.1662
Mean demand is 1.2 dollies per day and there is standard deviation = 1.1662 dollies
(b)
Mean of demand for Revenue = 0 * 0.35 + 0.30 * 40 + 0.2 * 80 + 0.1 * 80 + 0.05 * 80 = $40
Variance of demand for furniture dollies = 0.35 * (0-40)2 + 0.30 * (40 - 40)2 + 0.20 * (80-40)2 + 0.10 * (80 - 40)2 + 0.05 * (80 - 40)2 = 1120
Standard deviation of demand for furniture dollies = sqrt(1120) = 33.47
Mean revenue in this case is $ 40 and standard deviation of revenue = $33.47
(c)
Mean of demand for coupon cost = 0 * 0.35 + 0.30 * 0 + 0.2 * 0 + 0.1 * 15 + 0.05 * 30 = $3
Variance of demand for furniture dollies = 0.35 * (0-3)2 + 0.30 * (0 - 3)2 + 0.20 * (0-3)2 + 0.10 * (15 - 3)2 + 0.05 * (30 - 3)2 = 58.5
Standard deviation of demand for furniture dollies = sqrt(58.5) = $7.65
Mean revenue in this case is $ 3 and standard deviation of revenue = $7.65
(d) Expected Profit for furniture dollies = Expected revenue - Expected cost = $ 40 - $ 3 = $37
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