A bicycle shop plans to offer 2 specially priced children\'s models at a sidewal

Question

A bicycle shop plans to offer 2 specially priced children's models at a sidewalk sale. The basic model will return a profit of $100 and the deluxe model $180. Past experience indicates that sales of the basic model will have a mean of 5.3 bikes with a standard deviation of 1.3, and sales of the deluxe model will have a mean of 3.6 bikes with a standard deviation of 0.5 bikes. The cost of setting up for the sidewalk sale is $500. Complete parts a) through d). a) Define the random variables and use them to express the bicycle shop's net profit. A. B = number of basic bicycles sold, D = number of deluxe bicycles old, Profit = 100B + 180D - 500 B. B = price of the basic bicycle, D = price of a deluxe bicycle, Profit = 5.3B + 3.6D C. B = number of basic bicycles sold, D = number of deluxe bicycles old, Profit = 100B + 180D D. B = price of the basic bicycle, D = price of a deluxe bicycle, Profit = 5.3B + 3.6D - 500 b) What is the mean of the net profit? The mean profit is $. c) What is the standard deviation of the net profit? d) Do you need to make any assumptions in calculating the mean? A. Yes; the variables must be discrete. B. Yes, the sales must be independent. C. Yes; the sales must be dependent. D. No; no assumptions are made in calculating the mean. Do you need to make any assumptions in calculating the standard deviation? A. Yes; the sales must be dependent. B. Yes; the sales must be independent. C. Yes; the variables must be discrete. D. No; no assumptions are made in calculating the standard deviation.

Explanation / Answer

(A) B = Number of basic bicycles ; D = Number of deluxe bicycles

Profit = 100 B + 180 D - 500

(B) Mean net profit = 100 * 5.3 + 180 * 3.6 - 500 = $ 678

(C) First we will calculate variance of profit then we will calculate standard deviation

Variance of profit = (100 * 1.3) 2 + (180 * 0.5)2 = 25000

Std. Dev. of profit = sqrt (variance) = $ 158.11

(D) There is one assumption while calculating mean is that the sales must be independent.

(E) similarly, for calculating standard deviation , sales values calculated must be independent.

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