Mathematics

Case Study Analysis I

1. A business executive, transferred from Chicago to Atlanta, needs to sell her house in Chicago quickly. The executive’s employer has offered to buy the house for $210,000, but the offer expires at the end of the week. The executive does not currently have a better offer but can afford to leave the house on the market for another month. From conversations with her realtor, the executive believes the price she will get by leaving the house on the market for another month is uniformly distributed between $300,000 and $325,000. (50 points)

(A) If she leaves the house on the market for another month, what is the mathematical expression for the probability density function of the sales price

(B) If she leaves it on the market for another month, what is the probability that she will get at least $315,000 for the house?

(C) If she leaves it on the market for another month, what is the probability that she will get less than $310,000?

(D) What is the expected value of sales price?

(E) Should the executive leave the house on the market for another month? Why or why not? Develop your answers based on the results from (A)-(D), using at least 100 words.

2. The U.S. Bureau of Labor Statistics reports that the average annual expenditure on food and drink for all families is $5,700 (Money, December 2003). Assume that annual expenditure on food and drink is normally distributed and that the standard deviation is $1,500. (20 points)

(A) What is the range of expenditures of the 24.2% of families with the lowest annual spending on food and drink?

(B) Assume total number of families is 500,000. How many families spend more than $7000 annually on food and drink?

3. The average base salary for a store manager (Wal-Mart) in Riverside, California, is $68,000, and the average base salary for a store manager (Wal-Mart) in Los Angeles, California, is $78,000. Assume that salaries are normally distributed, the standard deviation for store managers in Riverside is $20,000, and the standard deviation for store managers in Los Angles is $22,000. (55 points)

(A) What is the probability that a store manager in Riverside has a base salary in excess of $100,000?

(B) What is the probability that a store manager in Los Angeles has a base salary in excess of $100,000?

(C) What is the probability that a store manager in Los Angeles has a base salary of less than $67,000?

(D) How much would a store manager in Los Angeles have to make in order to have a higher salary than 98.21% of the store managers in Riverside?

(E) Based the results from (A)-(D), if you are a job applicant for store manager position (Wal-Mart) in California, how would you negotiate annual salary using at least 200 words.

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