Probability Random Variables Double Check Please

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• Jul 31st 2009, 08:28 PM
rice4lifelegit
Probability Random Variables Double Check Please
A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of \$100 a year plus a \$25 service charge for each repair needed. The company’s research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.
a)Find the expected number of repairs this kind of computer is expected to need each year. Show your work.
My answer: .200

X | P(x) | xP(x) |
0 | .86 | 0 |
1 | .09 | .09 |
2 | .04 | .08 |
3 | .01 | .03 |

0 + .09 + .08 + .03 = .200

b)Find the standard deviation of the number of repairs each year.
My answer: .54772
.0344+.0576+.1296+.0784 = .54772

c)What are the mean and standard deviation of the company’s annual expense for the service contract? HINT: Annual expense Y = 100 + 25 ´ X, where X = number of repairs.
My answer:

Mean= 105
Std Dev = 13.675

d)The service contract for the printer estimates a mean annual cost of \$120 with standard deviation of \$30. What is the expected value and standard deviation of the total cost for the service contracts on computer and printer? On what assumption does your calculation rest?
My Thoughts:

Would I just add 120 to the annual expenses for a computer in the previous problem and then calculate the expected value and standard deviation? If so, what is the point of the std deviation of \$30 given to me in the problem?
• Aug 2nd 2009, 02:25 PM
CaptainBlack
Quote:

Originally Posted by rice4lifelegit
b)Find the standard deviation of the number of repairs each year.
My answer: .54772
.0344+.0576+.1296+.0784 = .54772

That answer is correct, but the calculation you give does not give that answer.

CB
• Aug 2nd 2009, 06:06 PM
rice4lifelegit
Quote:

Originally Posted by CaptainBlack
That answer is correct, but the calculation you give does not give that answer.

CB

Sorry My mistake, I mean sqrt(.0344+.0576+.1296+.0784) = .54772