A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What percentage of adults do not conduct their banking online? B. What type of probability is the 25% mentioned above? Just write down the name of the probability. C. Construct a joint probability table showing all joint and marginal probabilities.
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- A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online.
A. What percentage of adults do not conduct their banking online?
B. What type of probability is the 25% mentioned above? Just write down the name of the probability.
C. Construct a joint probability table showing all joint and marginal probabilities.
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- Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.A new edition of a very popular textbook will be published a year from now. The publisher currently has 1000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution in the file P10_31.xlsx. A production run incurs a fixed cost of 15,000 plus a variable cost of 20 per book printed. Books are sold for 190 per book. Any demand that cannot be met incurs a penalty cost of 30 per book, due to loss of goodwill. Up to 1000 of any leftover books can be sold to Barnes and Noble for 45 per book. The publisher is interested in maximizing expected profit. The following print-run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with remaining sales of the current edition will be between what two values?Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)
- Peter Martin will help his brother who wants to open a grocery store. Peter initially believes there is a 50-50 chance that his brother's food store will be successful. Peter is considering doing market research. Based on historical data, there is a 0.8 probability that the market research will be favorable given a successful store. Furthermore, there is a 0.7 probability that the market research will be unfavorable given an unsuccessful store. a) If the market research is favorable, what is Peter's revised probability of a successful store for his brother?b) If the market survey is unfavorable, what is Peter's revised probability of a successful store for his brother?c) If the initial probability of a successful store is 0.60 (instead of 0.50), find the probabilities of (a) and (b).The Valley Wine Company purchases grapes from either of two nearby grape growers each season to produce a particular red wine. It purchases enough grapes to produce 3000 bottles of the wine. Each grower supplies a certain portion of poor quality grapes, resulting in a percentage of bottles being used as fillers for cheaper table wines according to the following probability distribution. Probability of Percent Defective Defective (%) Grower A Grower B 2 .15 .30 4 .20 .30 6 .25 .20 8 .30 .10 10 .10 .10 The two growers charge a different prices for their grapes and because of differences in taste, the company charges different prices for their wine depending on which grapes they use. The annual profit from the wine produced from each grower's grapes for each percentage defective is as follows. PROFIT DEFECTIVE GROWER A GROWER B 2% $44,200 $42,600 4 40,200 40,300 6 36,200 38,000 8 32,200 35,700 10 28,200 33,400 Use decision-tree…In 1996, McDonald’s (MD) launched Campaign 55, reducing the prices ofits “flagship” sandwiches with the objective of regaining market share. Beforethe launch, suppose MD’s management envisioned two possible outcomes: astrong customer response or a weak response. Industry experts were notvery optimistic about the campaign. They assessed the probability of a strong response to be .40. MD predicted an expected profit of $50 million if theresponse proved to be strong. If the immediate customer response was weak,management believed that all was not lost. If MD could persuade themajority of its franchisees to back and help fund the campaign, the resultingprofit would be $20 million. However, if the majority rose up against thecampaign, the red ink would fly, and McDonald’s profit would be -$100million. MD considered these two outcomes to be equally likely.a. Given these assessments, construct a decision tree to determine MD’sexpected-profit-maximizing course of action.b. Suppose that MD has…
- Deborah Kellogg buys Breathalyzer test sets for the Denver Police Department. The quality of the test sets from her two suppliers is indicated in the following table: percent defective probability for winter park probability for technology dayton enterprise 1% 0.65 0.25 3% 0.25 0.25 5% 0.10 0.50 For example the probability of getting a batch of tests that are 1% defective from Winter park technology is 0.65. Because Kellogg orders 10,000 tests per order, this would mean there is a 0.65 probability of getting 100 defective tests out of the 10,000 tests if Winter park technology is used to fill the order. A defectice breathalyzer test can be repaired for $0.50. Although the quality of the…A company wants to produce a souvenir with a marketing life of sixmonths. Uncertainty surrounds the likely sales volume as well as thefixed costs of the venture as shown below:Sales units Probability Contrn. /unit Probability Fixed cost Probability100 000 0.3 K 7 0.5 K400 000 0.2 Page 5 of 80 000 0.6 K 5 0.5 K450 000 0.560 000 0.1 K500 000 0.31.0 1.0 1.0 Determine the expected value of the contributionA national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. A. What is the probability that an individual conducts banking online given that the individual is under the age of 50? B. Are Banking Online and Age independent? Explain.
- A metropolitan school system consists of two districts, east and west. The east district contains 35% of all students, and the west district contains the other 65%. A vocational aptitude test was given to all students; 10% of the east district students failed, and 25% of the west district students failed. Given that a student failed the test, what is the posterior probability that the student came from the east district?Cost Estimation; High-Low and Regression Methods The Mac Davis Company specializesin the purchase, renovation, and resale of older homes. Mac employs several carpenters and paintersto do the work for him. It is essential for him to have accurate cost estimates so he can determinetotal renovation costs before he purchases a piece of property. If estimated renovation costs plus thepurchase price of a house are higher than the house’s estimated resale value, it is not a worthwhileinvestment.Mac has been using the home’s interior square feet for his exterior paint cost estimations. Recentlyhe decided to include the number of external openings—the total number of doors and windows ina house—as a cost driver. Their cost is significant because they require time-consuming preparatorywork and careful brushwork. The rest of the house usually is painted either by rollers or spray guns,which are relatively efficient ways to apply paint to a large area. Mac has kept careful records of theseexterior…