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Math Help - AP Stat help!

  1. #1
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    AP Stat help!

    I think a-c are correct, but I am completely lost on d-g

    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.

    .200

    b)Find the standard deviation of the number of repairs each year.

    .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.

    Mean= 105
    Std Dev = 13.675

    d)How many times should the company expect to have to get this computer repaired over the three-year term of the lease?

    no idea.

    e)What is the standard deviation of the number of repairs that be required during the three-year lease period? On what assumption does your calculation rest. Do you think that this assumption is reasonable?

    no idea.


    f)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?

    no idea.

    g)Which service contract should the company expect to cost more each year? How much more? With what standard deviation?

    no idea.
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  2. #2
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    d)How many times should the company expect to have to get this computer repaired over the three-year term of the lease?
    Just simple multiplication. 3 times the expectation that he will have to get it repaired in one year.

    e)What is the standard deviation of the number of repairs that be required during the three-year lease period? On what assumption does your calculation rest. Do you think that this assumption is reasonable?
    Do you know how to do linear transformations of means, std, variance, etc.? That's all you are doing here. Multiplying by a scalar 3. However the effect that is has on the mean (just multiply by three), is not the same as it has on the std and variance.

    f)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?
    If the printer fails, is that going to affect the computer failing?

    g)Which service contract should the company expect to cost more each year? How much more? With what standard deviation?
    Yes you do. You already calculate the EXPECTED cost of one, and they give you the EXPECTED cost of the other.
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  3. #3
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    thank you so much for your help, i was wondering if you could give me input on what i came up with...

    Quote Originally Posted by ANDS! View Post
    Just simple multiplication. 3 times the expectation that he will have to get it repaired in one year.
    0.6




    Do you know how to do linear transformations of means, std, variance, etc.? That's all you are doing here. Multiplying by a scalar 3. However the effect that is has on the mean (just multiply by three), is not the same as it has on the std and variance.
    So would it be ".55*3=1.65. My calculations rest on the assumption that the standard deviation is the same every year. This assumption is not reasonable." ?




    If the printer fails, is that going to affect the computer failing?
    I don't understand what you're saying...

    should I add the costs (100+120) and std. deviations (13.68+30)???




    Yes you do. You already calculate the EXPECTED cost of one, and they give you the EXPECTED cost of the other.
    Printer, $15, and i dont know what to do for the standard deviation...
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