A retail company operates two types of clothing stores in shopping malls. One type specializes in clothes for men, and the other in clothes for women. The sales from a men’s clothing store average $800,000 annually and those from a women’s clothing store average $675,000 annually. The standard deviation of sales among men’s stores is $100,000 annually, and among women’s stores is $125,000. In a typical mall, the company operates one men’s store and one women’s store (under different names).
(a) What are the expected annual sales for the stores owned by this company in one shopping mall?
(b) Would you expect to find that the sales in the stores are positive or negatively correlated, or do you expect to find that the sales are uncorrelated?
(c) If the company operated two women’s stores rather than one of each type, would you expect the dependence between the sales at the two women’s clothing stores to be positive or negative or near zero?
(d) Find the standard deviation of the total sales if the correlation between the sales at the men’s store and women’s store is ρ = 0.4.
(e) The rent for the space in the shopping mall costs $30 per square foot. Both types of stores occupy 2,500 square feet. What is the expected value and standard deviation of total sales in excess of the rent costs?
(f) If labor and other expenses (such as the cost of clothing that is sold) to operate the two stores at the mall costs the company $750,000 annually, do you think there is a good chance that the company might lose money?