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Math Help - Finding Total Cost Mean Std Deviation

  1. #1
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    Finding Total Cost Mean Std Deviation

    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)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?

    Would I just find the mean cost and standard deviation for the computer and just add the two. So for computer Mean = 105 Dev= 13.675 so add (120+105) + (13.675+30)? thus equals = 268.675 for total cost?
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  2. #2
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    Is this the exact question. Are they saying WITHOUT a repair contract, the annual cost to maintain the printer (and I'm assuming the computer as well) would be $120.00 (with a standard deviation of $30)?

    Is this the entirety of the question? Do you know how to find the EXPECTED VALUE of something?

    Would I just find the mean cost and standard deviation for the computer and just add the two. So for computer Mean = 105 Dev= 13.675 so add (120+105) + (13.675+30)? thus equals = 268.675 for total cost?
    No. Mean and standard deviation can not be added like this. What class is this in, so we can get some background on what they might be expecting of you (calculation wise).
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  3. #3
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    You can't add the mean to the standard deviation. I'm guessing the assumption for the calculation is that they are independent and identically distributed random variables?

    You can add mean to mean.

    For independent random variables X and Y, the variance of their sum or difference is the sum of their variances
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