A collector is selling a quantity of action figures at an online auction. He has

Question

A collector is selling a quantity of action figures at an online auction. He has 18 cowboy figures. In recent auctions, the mean selling price of similar figures has been $12.39, with a standard deviation of $1.49. He also has 11 Indian figures which have had a mean selling price of $10.03, with a standard deviation of $0.86. His insertion fee will be $0.60 on each item, and the closing fee will be 8.25% of the selling price. He assumes all will sell without having to be relisted. Complete parts a through d.

b) ) Find the mean (expected value) of the net revenue

c) Find the standard deviation of the net revenue.

Explanation / Answer

Mean of net revenue will be 18*12.39 *(1-8.25%) + 11*10.03*(1-8.25%) - 0.60(18+11) = 288.49

Note, 1- 8.25% term is added to account for commission

The last term is 0.60 dollars per item multiplied by number of items

Standard deviation of net revenue will be Sqrt(1-8.25%) * Sqrt((18/29)^2 * sigma cowboy^2 + (11/29)^2 * sigma Indian ^2) = Sqrt(0.9175)* sqrt[ 18/29*18/29* 1.49^2 + 11/29*11/29*0.86*0.86] = 0.9393

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