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billyhilly billyhilly
wrote...
Posts: 479
5 years ago
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.

Find the expected number of repairs this kind of freezer is expected to need each year. Show your work.
Textbook 
Stats: Modeling the World

Stats: Modeling the World


Edition: 4th
Authors:
Read 311 times
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wrote...
5 years ago
E(X) = 0(0.80) + 1(0.11) + 2(0.05) + 3(0.04) = 0.33 repairs
wrote...
5 years ago
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.

Find the standard deviation of the number of repairs each year.
wrote...
5 years ago
Var(X) = (0 - 0.33)2(0.80) +  (1 - 0.33)2(0.11) +  (2 - 0.33)2(0.05) + (3 - 0.33)2(0.04) = 0.561
Standard Deviation = = 0.749
wrote...
5 years ago
Thank you for answering so quickly
wrote...
5 years ago
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.

What is the standard deviation of the number of repairs that may be required during the three-year term of the lease? On what assumption does your calculation rest? Do you think this assumption is reasonable?
wrote...
5 years ago
Var(X1 + X2 + X3) = 0.561 + 0.561 + 0.561 = 1.683, so standard deviation(C) = 1.297
The assumption is that the number of repairs is independent from year to year. This might be incorrect because some freezers might need more service than others.
wrote...
5 years ago
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.

The yearly service contract for the food fryer estimates a mean annual cost of $140 with a standard deviation of $40. What is the expected value and standard deviation of the total cost for the service contracts for the freezer and the food fryer?
wrote...
5 years ago
E(freezer + fryer) = $136.55 + $140 = $276.55
Var(freezer + fryer) = ($26.22)2 + ($40)2 = 2287.49, so standard deviation = $47.83
wrote...
5 years ago
Thanks for your help!
wrote...
5 years ago
A fast food restaurant just leased a new freezer and food fryer for three years. The service contract for the freezer offers unlimited repairs for a fee of $125 a year plus a $35 service charge for each repair needed. The restaurant's research suggested that during a given year 80% of these freezers need no repairs, 11% needed to be serviced once, 5% twice, 4% three times, and none required more than three repairs.

Which service contract should the restaurant expect to cost more each year? How much more? With what standard deviation?
wrote...
5 years ago
The food fryer's service contract is expected to cost more.
E(fryer - freezer) = $140 - $136.55 = $3.45 more
Standard deviation(fryer - freezer)  = $47.83  (same as the sum in problem 6)
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