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Math Help - Exponential Distribution question

  1. #1
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    Exponential Distribution question

    Q1. Mr. Michael Gates feels that the time to prepare an individuals
    income tax is exponentially distributed. In the past, he has noted
    40% of the returns are completed in 2 hours, 60% are completed in 4
    hours and 85% are completed in 8 hours. Estimate the mean time for
    the completion of a tax return.

    Please if someone can assist me to solve the problem. Many thanks.
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  2. #2
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    Quote Originally Posted by jovic1104 View Post
    Q1. Mr. Michael Gates feels that the time to prepare an individuals
    income tax is exponentially distributed. In the past, he has noted
    40% of the returns are completed in 2 hours, 60% are completed in 4
    hours and 85% are completed in 8 hours. Estimate the mean time for
    the completion of a tax return.

    Please if someone can assist me to solve the problem. Many thanks.
    Are we meant to assume from your post title that the time follows an exponential distribution? If so, then the mathemtaical translation of what you have written, namely, Pr(X = 2) = 0.4, Pr(X = 4) = 0.6 and Pr(X = 8) = 0.85 makes no sense.

    Surely you mean something like
    40% of the returns are completed in 2 hours or less, 60% are completed in 4
    hours or less and 85% are completed in 8 hours or less.


    Until you have clarified the situation there's nothing more that can be done.
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    Quote Originally Posted by mr fantastic View Post
    Are we meant to assume from your post title that the time follows an exponential distribution? If so, then the mathemtaical translation of what you have written, namely, Pr(X = 2) = 0.4, Pr(X = 4) = 0.6 and Pr(X = 8) = 0.85 makes no sense.

    Surely you mean something like
    [/COLOR]

    Until you have clarified the situation there's nothing more that can be done.
    Hi, thank you for your reply. About the question, that is the exact problem given from my notes. Can you show me how you got P=0.85? And let say the question was:

    40% of the returns are completed in 2 hours or less, 60% are completed in 4
    hours or less and 85% are completed in 8 hours or less.

    Can we have the correct solution? I am not sure what type of exponential distribution for this question is.

    Thanks for any feedback.
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  4. #4
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    Quote Originally Posted by jovic1104 View Post
    Hi, thank you for your reply. About the question, that is the exact problem given from my notes. Can you show me how you got P=0.85? Mr F says: What do yuo think the 85% in your question meant ....?

    And let say the question was:

    40% of the returns are completed in 2 hours or less, 60% are completed in 4
    hours or less and 85% are completed in 8 hours or less.

    Can we have the correct solution? I am not sure what type of exponential distribution for this question is.

    Thanks for any feedback.
    Exponential distribution - Wikipedia, the free encyclopedia

    I suppose you can use the given information in the revised question and the cdf of the exponential distribution to estimate the parameter \lambda.
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    Quote Originally Posted by jovic1104 View Post
    Hi, thank you for your reply. About the question, that is the exact problem given from my notes. Can you show me how you got P=0.85? And let say the question was:

    40% of the returns are completed in 2 hours or less, 60% are completed in 4
    hours or less and 85% are completed in 8 hours or less.

    Can we have the correct solution? I am not sure what type of exponential distribution for this question is.

    Thanks for any feedback.
    thanks for a very quick response. Sorry for my stupid question, 85% is 0.85 when converted to decimal. I will work for the solution in regards to cdf under exponential distribution.

    thanks again.
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