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Math Help - Probability Random Variables Double Check Please

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by rice4lifelegit View Post
    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
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    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
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