Individual Problem 7 Chapter 2 Problem 9: 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? Problem 15: During a recent period of high unemployment, hundreds of thousands of drivers dropped their automobile insurance. Sample data representative of the national automobile insur- ance coverage for individuals 18 years of age and older are shown her Automobile Insurance Yes No 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 individual 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? Problem 20: 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 Z 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) Chapter 3 Problem 11: A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large. The survey found that 74% of the respondents do believe inequality is too large. a. In a sample of six British citizens, what is the probability that two believe inequality is too large? b. In a sample of six British citizens, what is the probability that at least two respondents believe that inequality is too large? c. In a sample of four British citizens, what is the probability that none believe inequality is too large? Problem 15: 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? Problem 19: 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 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? Problem 25: The College Board National Office recently reported that in 2011-2012, the 547,038 high school juniors who took the ACT achieved a mean score of 530 with a standard deviation of 123 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf /research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed. a. what is the probability that a high school junior who takes the test will score at least 610 on the mathematics portion of the test? b. what is the probability that a high school junior who takes the test will score no higher than 460 on the mathematics portion of the test? c. what is the probability that a high school junior who takes the test will score between 460 and 550 on the mathematics portion of the test? d. how high does a student have to score to be in the top 10% of high school juniors on the mathematics portion of the test? Chapter 16 Problem 2: The management of Madeira Computing is considering the introduction of a wearable electronic device with the functionality of a laptop computer and phone. The fixed cost to launch this new product is $300,000. The variable cost for the product is expected to be between $160 and $240, with a most likely value of $200 per unit. The product will sell for $300 per unit. Demand estimates for the produce vary widely, ranging from 0 to 20,000 units, with an average of 4000 units. a. Compute profit for the base-case, worst-case, and best-case scenarios. b. Assume the variable cost is a uniform random variable between $16 and $24 and the product demand is an exponential random variable with a mean of 4000 units. Construct a simulation model to estimate the mean profit and the probability that the project will result in a loss. Problem 3: Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund a portion of the purchase price if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000. a. For each tire sold, what is the expected cost of the promotion? b. What is the probability that Grear will refund more than $50 for a tire? c. What mileage should Grear set the promotion claim if it wants the expected cost to be $2