Natway, a national distribution company of home vacuum cleaners, recommends that

Question

Natway, a national distribution company of home vacuum cleaners, recommends that its salespersons make only two calls per day, one in the morning and one in the afternoon. Twenty-five percent of the time a sales call will result in a sale, and the profit from each sale is $125. Develop the probability distribution for sales during a five-day week. What is the mean and variance of this distribution? What is the expected weekly profit for a salesperson?

Note: I want this question to be answered in excel format.

Explanation / Answer

here probabilty of 0 profit =P(0 sales) =P(X=0) =binomdist(0,2,0.25,false) =0.5625

probabilty of $125 profit =P(1 sales) =P(X=$125) =binomdist(1,2,0.25,false) =0.375

probabilty of $250 profit =P(2 sales) =P(X=$250) =binomdist(2,2,0.25,false) =0.0625

therefore from above :

mean of sales during a five-day week =5*62.50=312.5

variance of sales during a five-day week =5*5859.3750=29296.875

expected weekly profit for a salesperson =$312.5

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 0 0.5625 0.000 0.000 3906.250 2197.266 125 0.3750 46.875 5859.375 3906.250 1464.844 250 0.0625 15.625 3906.250 35156.250 2197.266 total 1 = 62.50 9765.625 42968.750 2= 5859.3750

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