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 A bicycle shop plans to offer 2 specially priced​ children's models at a sidewalk sale. The basic model will return a profit of ​$110 and the deluxe model ​$130. Past experience indicates that sales of the basic model will have a mean of 5.1 bikes with a standard deviation of 1.4​, and sales of the deluxe model will have a mean of 3.7 bikes with a standard deviation of 0.7 bikes. The cost of setting up for the sidewalk sale is ​$400. 

d) Do you need to make any assumptions in calculating the​ mean?

--  No; no assumptions are made in calculating the mean.

Do you need to make any assumptions in calculating the standard​ deviation?

--  Yes; the sales must be independent.

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Define the random variables and use them to express the bicycle​ shop's net profit. 

B = number of basic bicycles​ sold, Upper D equals number of deluxe bicycles sold​, 
Profit equals 110B plus 130 D minus 400

b) What is the mean of the net​ profit?

110*5.1 + 130*3.7 - 400  = 642

c. The standard deviation of the distribution

sqrt((110^2 * 1.4^2) + (130^2 *0.7^2)) = 178.88

 

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