Reference no: EM132324241

Part -1:

Question 1: A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine; 250 patients with symptoms that included itchy eyes and a skin rash received the new drug. The results of the study are as follows: 90 of the patients treated experienced eye relief, 135 had their skin rash clear up, and 45 experienced relief of both itchy eyes and the skin rash. What is the probability that a patient who takes the drug will experience relief of at least one of the two symptoms?

Question 2: Hundreds of thousands of drivers dropped their automobile insurance in 2008 as the unemployment rate rose (Wall Street Journal, December 17, 2008). Sample data representative of the national automobile insurance coverage for individuals 18 years of age and older are shown here.

		Automobile Insurance
		Yes	No
Age	18 to 34	1500	340
	35 and over	1900	260

a. Develop a joint probability table for these data and use the table to answer the remaining questions.
b. What do the marginal probabilities tell you about the age of the U.S. population?
c. What is the probability that a randomly selected individual does not have automobile insurance coverage?
d. If the individual is between the ages of 18 and 34, what is the probability that the in dividual does not have automobile insurance coverage?
e. If the individual is age 35 or over, what is the probability that the individual does not have automobile insurance coverage?
f. If the individual does not have automobile insurance, what is the probability that the individual is in the 18-34 age group?
g. What does the probability information tell you about automobile insurance coverage in the United States?

Question 3: The prior probabilities for events A₁, A₂, and A₃ are P(A₁) = 0.20, P(A₂) = 0.50, and P(A₃) = 0.30. The conditional probabilities of event B given A₁, A₂, and A₃ are P(B | A₁) = 0.50, P(B | A₂)  = 0.40, and P(B A₃) = 0.30.

a. Compute P(B ∩ A₁), P(B ∩ A₂), and P(B ∩ A₃).

b. Apply Bayes' theorem, equation (2.16), to compute the posterior probability P(A₂ B).

c. Use the tabular approach to applying Bayes' theorem to compute P(A₁ B), P(A₂ | B), and P(A₃ B).

Part -2:

Question 1: 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?

Question  2:. Telephone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Find the probability of receiving 3 calls in a 5-minute interval.

b. Find the probability of receiving 10 calls in 15 minutes.

c. Suppose that no calls are currently on hold. If the agent takes 5 minutes to complete processing the current call, how many callers do you expect to be waiting by that time? What is the probability that no one will be waiting?

d. If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted?

Question 3: Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

a. Show the graph of the probability density function for flight times.
b. What is the probability that the flight will be no more than 5 minutes late?
c. What is the probability that the flight will be more than 10 minutes late?
d. What is the expected flight time?

Question 4: In 2003, the average stock price for companies making up the S&P 500 was $30, and the standard deviation was $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assume the stock prices are normally distributed.

a. What is the probability that a company will have a stock price of at least $40?

b. What is the probability that a company will have a stock price no higher than $20?

c. How high does a stock price have to be to put a company in the top 10%?

Part 3:

Question 1. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is expected to be between $16 and $24, with a most likely value
of $20 per unit. The product will sell for $50 per unit. Demand for the product is expected to range from 300 to 2100 units, with 1200 units the most likely demand.
a. Develop the profit model for this product.
b. Provide the base-case, worst-case, and best-case analyses.
c. Discuss why simulation would be desirable.

Question 2. a. Use the random numbers 0.3753, 0.9218, 0.0336, 0.5145, and 0.7000 to generate five simulated values for the PortaCom direct labor cost per unit.
b. Use the random numbers 0.6221, 0.3418, 0.1402, 0.5198, and 0.9375 to generate five simulated values for the PortaCom parts cost.
c. Use the random numbers 0.8531, 0.1762, 0.5000, 0.6810, and 0.2879 and the table for the cumulative standard normal distribution in Appendix D to generate five simulated values for the PortaCom first-year demand.

Question 3. The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. Probability distributions for the purchase cost, the labor cost, and the transportation cost are as follows:

Purchase Cost ($)	Probability	Labor Cost ($)	Probability	Transportation Cost ($)	Probability
10	0.25	20	0.1	3	0.75
11	0.45	22	0.25	5	0.25
12	0.3	24	0.35
		25	0.3

Assume that these are the only costs and that the selling price for the product will be $45 per unit.

a. Provide the base-case, worst-case, and best-case calculations for the profit per unit.

b. Set up intervals of random numbers that can be used to randomly generate the three cost components.
c. Using the random numbers 0.3726, 0.5839, and 0.8275, calculate the profit per unit.
d. Using the random numbers 0.1862, 0.7466, and 0.6171, calculate the profit per unit.
e. Management believes the project may not be profitable if the profit per unit is less than $5. Explain how simulation can be used to estimate the probability that the profit per unit will be less than $5.

Question 4. Develop a worksheet simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is uniformly distributed between $16 and $24 per unit. The product will sell for $50 per unit.

Demand for the product is best described by a normal probability distribution with a mean of 1200 units and a standard deviation of 300 units. Develop a spreadsheet simulation similar to Figure 16.6. Use 500 simulation trials to answer the following questions:

a. What is the mean profit for the simulation?
b. What is the probability that the project will result in a loss?
c. What is your recommendation concerning the introduction of the product?