× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
5
a
5
k
5
c
5
B
5
l
5
C
4
s
4
a
4
t
4
i
4
r
4
Home Q & A Board Science-Related Homework Help Mathematics Statistics and Probability
New Topic  
billyhilly billyhilly
wrote...
Posts: 479
Rep: 11 0
4 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 284 times
11 Replies

Related Topics

Replies
wrote...
#1
4 years ago
E(X) = 0(0.80) + 1(0.11) + 2(0.05) + 3(0.04) = 0.33 repairs
wrote...
#2
4 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...
#3
4 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...
#4
4 years ago
Thank you for answering so quickly
wrote...
#5
4 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...
#6
4 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...
#7
4 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...
#8
4 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...
#9
4 years ago
Thanks for your help!
wrote...
#10
4 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...
#11
4 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)
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1300 People Browsing
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Related Images
  
 3370
  
 231
  
 203
Your Opinion
Which country would you like to visit for its food?
Votes: 204
Previous poll results: What's your favorite coffee beverage?