1. ## 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.

2. Originally Posted by jovic1104
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.

3. Originally Posted by mr fantastic
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.

4. Originally Posted by jovic1104
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 $\lambda$.

5. Originally Posted by jovic1104
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.