# 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

2797 Views

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.

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