Quantitative methods in business problem:

1. Consider a binomial experiment withn=10 andp=0.10.

a. Findf(0).

b. Findf(2).

c. Find P(x 2).

d. Find P(x 1).

e. Find E(x).

f. Find Var(x) ands.

2. A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.

a. In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

b. In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

c. In a sample of ten British citizens, what is the probability that none have boycotted goods for ethical reasons?

3. The demand for a new product is estimated to be normally distributed with =200 ands =40. Letxbe the number of units demanded, and find the following probabilities:

a.P(180x220)

b.P(x250)

c.P(x100)

d.What is the estimated demand with a probability of 90%?

4. The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.

a. What is the probability that the time between vehicle arrivals is 12 seconds or less?

b. What is the probability that the time between vehicle arrivals is 6 seconds or less?

c. What is the probability that there will be 30 or more seconds between arriving vehicles?

5. Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow:

Dealer	Monthly Cost	Mileage Allowance	Cost per Additional Mile
Hepburn Honda	$299	36,000	$0.15
Midtown Motors	$310	45,000	$0.20
Hopkins Automotive	$325	54,000	$0.15

Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her $10,764 if she drives 12,000 miles per year, $12,114 if she drives 15,000 miles per year, or $13,464 if she drives 18,000 miles per year.

• a-Construct a payoff table for Amy's problem.
• b-If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?
• c-Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach?

6- The Lake Placid Town Council decided to build a new community center to be used for conventions, concerts, and other public events, but considerable controversy surrounds the appropriate size. Many influential citizens want a large center that would be a showcase for the area. But the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium, and large.

Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three scenarios: worst case, base case, and best case. The worst-case scenario corresponds to a situation in which tourism drops substantially; the base-case scenario corresponds to a situation in which Lake Placid continues to attract visitors at current levels; and the best-case scenario corresponds to a substantial increase in tourism. The consultant has provided probability assessments of 0.10, 0.60, and 0.30 for the worst-case, base-case, and best-case scenarios, respectively.

The town council suggested using net cash flow over a 5-year planning horizon as the criterion for deciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5-year planning horizon have been developed. All costs, including the consultant's fee, have been included.

Center Size	Demand Scenario
Worst Case	Base Case	Best Case
Small	400	500	660
Medium	250	650	800
Large	400	580	990

1. a-What decision should Lake Placid make using the expected value approach?
2. b-What is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?