Question 1
Janice Morgan, age 32, is single and has no dependents. She is a freelance writer. In January 2011, Janice opened her own office located at 2751 Waldham road, Pleasat Hill, NM 88135. She called her buiness Writers Anonymous. Janice is a cash basis taxpayer. She lives at 132 Stone Avenue, Pleasant Hill, NM 88135. Her Social Security number is 123-45-6789. Janice wants to contribute to the Presidentual Election campaign fund. During 2011, Janice had the following income and expense items connected with her business: Income from sales of articles $105,000 Rent $16,500 Utilities $7,900 Supplies $1,800 Insurance $5,000 Travel (including meals of $1,200) $3,500 Janice purchased and placed in service the following fixed assets for her business: ? Furniture and fixtures (new) costing $17,000 on January 10, 2011. ? Computer equipment (new) costing $40,000 on July 28, 2011. Janice did not elect immediate expensing under 179. She elected not to take addional first year depreciation. Janice?s itemized deductions are as follows: State income tax $3,000 Home mortgage interest paid to First Bank $6,000 Property taxes on home $1,500 Charitable contributions $1,200 Janice did not keep a record of the sales tax she paid. The amount from the sales tax table is $437. Janice has interest income of $5,000 on certificates of deposit at Second Bank. Janice makes estimated tax payments of $17,000 for 2011. Compute Janice Morgan?s 2011 Federal income tax payable (or refund due.) If you use tax forms for your conputations, you will need forms 1040 and 4562 and schedules A,B,C, and SE.
Question 2
ESSAY Questions: 1. John H. Surratt was one of John Wilkes Booth?s alleged accomplices in the murder of President Lincoln. On April 29, 1865, the Secretary of War issued and caused to be published in newspapers the following proclamation: ?$25,000 reward for the apprehension of John H. Surratt and liberal rewards for any information that leads to the arrest of John H. Surratt.? On November 24, 1865, President Johnson revoked the reward and published the revocation in the newspapers. Henry B. St. Marie learned of the reward but left for Rome prior to its revocation. In Rome, St. Marie discovered Surratt?s whereabouts. In April, 1866 unaware that the reward had been revoked, he reported this information to U.S. officials. Based on this information Surratt was arrested. The government denied St. Marie the reward. A. Should Marie have received the reward? Explain. Be sure to include in the discussion any theories of recovery Marie would argue as well as those the government would use to defeat Marie. B.If Marie were to get the award, would he be entitled to the full $25,000? Explain? C) What if this had occurred in the year 2010 and the reward was published not in a newspaper but on the Internet as was the revocation. Would the result be the same? Would it be the same if the award was published on the Internet, but the revocation in the newspaper? Explain 2. Joe Alexander contracted with Robert Harris for the sale of Harris?s business on February 1, 1988. Alexander purported to act on behalf of J&R Construction, a newly formed corporation. As the incorporators, Joe and Rita Alexander and Avanell Looney signed the articles of incorporation for J&R on the same day that Joe contracted with Harris. The Articles were not filed until February 3, 1988. When J&R defaulted on its payments due under the contract with Harris in 1991, Harris sued both Alexander and Looney personally for the $49,696, 21 still owed. The trial court held Joe Alexander personally liable because Joe had signed the contract with Harris. They did not hold Rita or Looney liable because the corporation had not yet come into existence. Harris appealed. A) Under what legal theory should Harris base his appeal? B) What should the court decide? Short Answer: 3 A) As a beginning songwriter and performer, you are convinced that a certain model of guitar is what you need to turn the musical world on its ear. Chick's Music store advertises the item but because the store is sold out when you get there, you accept a rain check signed by Daria, one of the employees. You return to the store one month later, but Chuck refuses to honor the rain check. Under the UCC would you win your suit to enforce the contract? Why or Why not? 3 B) On May 1, you contract orally with Johnny, a salesperson with Keyboards Emporium, to buy for $450 an electric organ for your personal enjoyment with delivery to occur on July 1. On May 15, you ask for delivery on June 1 and Johnny agrees. But delivery does not occur on June 1. The store later tells you delivery will be on July 1 as agreed in the first place. Under the UCC which delivery date is binding? Explain. Would there be a difference under common law contracts? Explain 3C) On the morning of October 2, 1989 a fire started by an arsonist broke out in the Red Inn in Provincetown, Massachusetts. The inn had smoke detectors, sprinklers, and an alarm system, all of which alerted the guests, but there were no emergency lights or clear exits. Attempting to escape, Deborah Addis and James Reed, guests at the inn, found the first-floor doors and windows locked. Ultimately, they forced open a second-floor window and jumped out. To recover for their injuries, they file suit in Massachusetts state court against Tamerlane Corporation, which operated the inn under a lease, the owners of the inn, and Diane Steel, an employee of the inn. Under what tort theory might Addis and Reed recover damages from Tamerlane and the others? What must they prove to recover damages under the theory? Discuss fully MULTIPLE CHOICES WITH AN EXPLANATION: 1) Red Owl Stores, Inc induced the Hoffmans to give up their current successful business to run a Red Owl Franchise. Although no contract was ever signed, the Hoffmans incurred numerous expenses in excess of $5,000 based on Red Owl?s representations. When the deal ultimately fell through because of Red Owl?s failure to keep its promise concerning the operation of the franchise agency store, the Hoffmans brought suit to recover their losses from the business they left behind and their out of pocket expenses on the Red Owl project. Will the Hoffmans recover any or all of their money? A) No, the Hoffmans cannot recover anything because the Statute of Frauds should apply. B) No, because the business they left behind was not part of the contract with Red Owl. C) Yes, the can recover everything under the doctrine of promissory estoppel. D) Yes, they can recover their out of pocket expenses on the Red Owl project because they relied to their detriment on Red Owl. 2. Owens, a federal prisoner, was transferred from federal prison to the Nassau County Jail pursuant to a contract between the U.S. Bureau of Prisons and the county. The contract included a policy statement that required the receiving prison to provide for the safekeeping and protection of the transferred federal prisoners. While in the Nassau County Jail, Owens was beaten severely by prison guards and suffered lacerations, bruises, and a lasting impairment that caused blackouts. Can Owens, as a third party beneficiary, sue the county for breach of its agreement with the U.S. Bureau of Prisons? A) Yes, because the intention to benefit a third party may be gleaned from the contract as a whole. B) No, because while the contract implies the intention to benefit a third party it does not specifically identify which party. C) Yes, because the contract was made to benefit third parties and it is not necessary to identify the third party. D) No, because Owen was a mere incidental beneficiary to the contract. 3) Patricia Aiken suffered a heart attack and was hospitalized at Phoenix Baptist Hospital and Medical Center, Inc. Later she passed away. At the time of her admission, the Aikens told the hospital that they did not have the money to pay for medical care. At the same time, Patricia?s husband, Thomas, signed an agreement to pay her medical expenses. He did not read what he signed, no one explained the agreement and he later claimed that he was so upset that he couldn?t remember signing anything. When the bills were not paid, the hospital filed suit. Will the Aikens have to pay the hospital? A) Yes, because the hospital relied on the signed agreement and performed. B) No, because while there was a written agreement the performance resulted in Mrs. Aikens demise. C) Yes, because even though the hospital was aware of the Aiken?s lack of funds, Mr. Aiken should have known when he took his wife to the hospital that they did not give care for free. D) No, because the agreement was an adhesion contract obtained under circumstances that made it unenforceable and it was not explained to him at the time by the hospital. 4) Steven Lanci was involved in an automobile accident with an uninsured motorist. Lanci was insured with Metropolitan Insurance Co., although he did not have a copy of the insurance policy. Lanci told Metropolitan that he did not have a copy of the policy and entered into negotiations with them in the meantime. Ultimately Lanci settled for $15,000, noting in a letter to Metropolitan that this was the ?sum you represented to be the?policy limits applicable to the claim.? After signing a release, Lanci learned that the policy limits were actually $250,000 and he refused to accept the settlement proceeds. Lanci argued that the release had been signed as a result of a mistake and therefore is unenforceable. Should the court enforce the contract? A) Yes, because Lanci as a reasonable person should have known what the policy limits were. B) Yes, because Lanci entered into the negotiations knowing that he did not have a copy of the policy and he assumed the risk of being unprepared. C) No, because ethically Metropolitan should have given him another copy before the negotiations. D) No, because Metropolitan knew the policy limits, knew that Lanci thought them to be $15,000 and that he entered into the contract because of that mistake of a material fact. 5) IBM hires only men under the age of 35 to sell their office machines. They do so because they know that most office machines are purchased by females under the age of 40. Tina applied for a sales position but is turned down. She files suit claiming she is being discriminated against because of her age, 36, and sex.5) a) she will be successful because selling office machines is a job that can be done by both sexes and at any age. b) she will succeed because she is almost 35 and her sex is irrelevant. c) she will loose because she has to be over 40 to sue for age discrimination according to the age Discrimination Act. d) she will loose because the corporation has a valid business reason for employing young male salesmen. 6) Glen Grove brought a 1936 Pontiac from Bernard Stanfield. Stanfield signed the certificate of title, which stated that the car was sold for $1,000. No other terms of sale were mentioned in the certificate, and none were incorporated by reference. Three years later, Stanfield filed suit against Grove in a Missouri State Court, claiming that Grove still owed $9,000 for the price of the car. At trial, Stanfield testified that he and Grove had an oral agreement by which Grove was to pay $1,000 for the ?title document? and $9,000 for the actual car. The court entered a judgment for Stanfield. What will happen on appeal? A) The court will uphold the entrance of the parole evidence and keep the verdict for Stanfield intact. B) The court will uphold the verdict for Stanfield because the writing was not sufficient enough to constitute a written contract so oral evidence can be heard to explain the terms of the agreement. C) The court will overturn the verdict of the lower court because the title is a legally sufficient document to form a contract. Oral evidence should not be allowed to amend the terms of the contract. D) The court will overturn the verdict because any reasonable person would have not turned the title over to someone else without getting all his money. Giving more money to Stanfield would unjustly enrich him. 7) John Agosta and his brother Salvatore had formed a corporation, but disagreements between the two brothers caused John to petition for voluntary dissolution of the corporation. According to the dissolution agreement, the total assets of the corporation, which included a warehouse and inventory, would be split between the two brothers by Salvatore?s selling his stock to John for $500,000. The agreement was approved, but shortly before payment was made, a fire destroyed the warehouse and inventory which were the major assets of the corporation. John refused to pay Salvatore the $500,000, and Salvatore brought suit against him for breach of contract. Will John win? A) Yes, because the value of the stock he is purchasing is not worth $500,000 anymore due to the fire. B) Yes, because the court cannot require him to specifically perform to Salvatore?s unjust enrichment. C) No, because the agreement was for the sale of stock not a functional business. D) No, The subject matter of the agreement, the shares of stock was not destroyed in the fire. The doctrine of impossibility of performance does not apply and John cannot avoid his contract. 8) Southeast Shipping Company challenges an Alabama statute, claiming that it unlawfully interferes with interstate commerce. A court will likely a) balance Alabama's interest in regulating against the burden on interstate commerce. b) balance the burden on Alabama against the merit and purpose of interstate commerce c) strike the statute. d) uphold the statute. 9) Donna the owner of Eagle Sales, a sole proprietorship, wants to increase the business?s capital without sacrificing control. This can be done most successfully by a) borrowing funds. b) bringing in partners. c) issuing stock. d) selling the business. 10) Nu Produx Inc (NPI) agrees to sell 100 cell phones to MYTALK Cell Service. NPI identifies the goods by marking the crate with red stripes. Before the crate is shipped, an insurable interest exists in a) Not NPI or MyTalk. b) NPI and My Talk. c) NPI only. d) MyTalk only.
Question 3
**Please submit formulas used & any explanations that may be necessary** (Interest-rate risk) A quick look at bond quotes will tell you that GMAC has many different issues of bonds outstanding. Suppose that four of them have identical coupon rates of 7.25% but mature on four different dates. One matures in 2 years, one in 5 years, one in 10 years, and the last in 20 years. Assume that they all made coupon payments yesterday. a. If the yield curve were flat and all four bonds had the same yield to maturity of 9%, what would be the fair price of each bond today? b. Suppose that during the first hour of operation of the capital markets today, the term structure shifts and the yield to maturity of all these bonds changes to 10%. What is the fair price of each bond now? c. Suppose that in the second hour of trading, the yield to maturity of all these bonds changes once more to 8%. Now what is the fair price of each bond? d. Based on the price changes in response to the changes in yield to maturity, how is interest-rate risk a function of the bond?s maturity? That is, is interest-rate risk the same for all four bonds, or does it depend on the bond?s maturity?
Question 4
Sales and Production Budgets (8-12): The marketing department of Jessi Corporation has submitted the following sales forecast for the upcoming fiscal year (all sales are on account): 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Units to be produced 12,000 14,000 13,000 11,000 The selling price of the company's product is $18.00 per unit. Management expects to collect 65% of sales in the quarter in which the sales are made, 30% in the following quarter, and 5% of sales are expected to be "'uncollectible. The beginning balance of accounts receivable, all of which is expected to be collected in the first quarter, is $70,200. The company expects to start the first quarter with 1,650 units in finished goods inventory. Management desires an ending finished goods inventory in each quarter equal to 15% of the next quarter's budgeted sales. The desired ending finished goods inventory for the fourth quarter is 1,850 units. Prepare the company's sales budget and schedule of expected cash collections. Prepare the company's production budget for the upcoming fiscal year. Direct Materials and Direct Labor Budgets (8-13): The production department of Hareston Company has submitted the following forecast of units to be produced by quarter for the upcoming fiscal year: 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Units to be produced 7,000 8,000 6,000 5,000 In addition, the beginning raw materials inventory for the first quarter is budgeted to be 1,400 pounds and the beginning accounts payable for the first quarter is budgeted to be $2,940. Each unit requires 2 pounds of raw material that costs $1.40 per pound. Management desires to end each quarter with an inventory of raw materials equal to 10% of the following quarter's production needs. The desired ending inventory for the fourth quarter is 1,500 pounds. Management plans to pay for 80% of raw material purchases in the quarter acquired and 20% in the following quarter. Each unit requires 0.60 direct labor-hours and direct labor-hour workers are paid $14.00 per hour. Prepare the company's direct materials budget and schedule of expected cash disbursements for purchases of materials for the upcoming fiscal year. Prepare the company's direct labor budget for the upcoming fiscal year, assuming that the direct labor workforce is adjusted each quarter to match the number of hours required to produce the forecasted number of units produced. Direct Labor and Manufacturing Overhead Budgets (8-14): The production department of Raredon Corporation has submitted the following forecast of units to be produced by quarter for the upcoming fiscal year: 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Units to be produced 12,000 14,000 13,000 11,000 Each unit requires 0.70 direct labor-hours, and direct labor-hour workers are paid $10.50 per hour. In addition, the variable manufacturing overhead rate is $1.50 per direct labor-hour. The fixed manufacturing overhead is $80,000 per quarter. The only noncash element of manufacturing overhead is depreciation, which is $22,000 per quarter. Prepare the company's direct labor budget for the upcoming fiscal year, assuming that the direct labor workforce is adjusted each quarter to match the number of hours required to produce the forecasted number of units produced. Prepare the company's manufacturing overhead budget.
Question 5
1. ?/3 points Notes At a party there are 37 students over age 21 and 22 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed. What is the chance? students over age 21 students under age 21 chance Why is your sample not an SRS? These combinations of students have equal chances of being interviewed. Not all combinations of students have an equal chance of being interviewed. All combinations of students have an equal chance of being interviewed. The sample size is too small. 2. ?/5 points Notes A chemical engineer is desiging the production process for a new product. The chemical reaction that produces the product may have higher or lower yield, depending on the light, temperature, and stirring rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of combinations of light levels (), two temperatures (40?C and 50?C) and four stirring rates (30 rpm, 60 rpm, 90 rpm, and 120 rpm) on the yield of the process. She will process four batches of the product at each combination of temperature and stirring rate. (a) What are the experimental units in this experiment? the yield of each batch the stirring rate the temperature the batches of the product What is the response variable in this experiment? the yield of each batch the temperature the batches of the product the stirring rate (b) How many factors are there? How many treatments are there? Use a diagram to lay out the treatments. (Do this on paper. Your instructor may ask you to turn in this work.) (c) How many experimental units are required for the experiment? 3. ?/4 points Notes The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 to a 30-meter circle of forest. We want to compare the growth in base area of trees in treated and untreated areas to see if extra CO2 does in fact increase growth. We can afford to treat three circular areas (a) Describe the design of a completely randomized experiment using 6 well-separated 30-meter circular areas in a pine forest. Sketch the circles and carry out the randomization your design calls for. If you used line 101 of Table B in your experiment, which areas would be treated? (Select all that apply.) 1 2 3 4 5 6 7 8 9 (b) Areas within the forest may differ in soil fertility. Describe a matched pairs design using three pairs of circles that will reduce the extra variation due to different fertility. Sketch the circles and carry out the randomization your design calls for. If you used line 125 of Table B in your experiment, which areas would be treated? (Use odds for the first area in each pair and evens for the second area. Select all that apply.) the first area in the first pair the first area in the second pair the first area in the third pair the second area in the first pair the second area in the second pair the second area in the third pair 4. ?/8 points Notes A basketball player makes 70% of her free throws in a long season. In a tournament game she shoots 5 free throws late in the game and misses 3 of them. The fans think she was nervous, but the misses may simply be chance. You will shed some light by estimating a probability. (a) Describe how to simulate a single shot if the probability of making each shot is 0.7. Then describe how to simulate 5 independent shots. (b) Simulate 50 repetitions of the 5 shots and record the number missed on each repetition. Use Table B starting at line 126. (Use the highest possible digits to represent misses. Use single digit numbers. Enter the frequency of your results. Let X represent the number of misses.) X 0 1 2 3 4 5 Frequency What is the approximate likelihood that the player will miss 3 or more of the 5 shots? 5. ?/3 points Notes Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has 8 out of 10 chances of passing on any one attempt by luck. What is Elaine's likelihood of passing on at least one of the three attempts? (Assume the attempts are independent because she takes a different examination on each attempt.) (a) Explain how you would use random digits to simulate one attempt at the exam. Elaine will of course stop taking the exam as soon as she passes. (b) Simulate 50 repetitions. What is your estimate of Elaine's likelihood of passing the course? (c) Do you think the assumption that Elaine's likelihood of passing the exam is the same on each trial is realistic? Why? No, learning usually occurs in taking an exam. Yes, the test should be on the same knowledge each time. No, she will have studied more before the first test. Yes, Elaine is still the same person from test to test. 6. ?/3 points Notes Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2000. Color: Silver White Black Dark green Dark blue Medium red Probability: 0.177 0.173 0.114 0.087 0.086 0.064 (a) What is the probability that the vehicle you choose has any color other than the six listed? (b) What is the probability that a randomly chosen vehicle is either silver or white? (c) Choose two vehicles at random. What is the probability that both are silver or white? 7. ?/2 points Notes Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV. Test result +- Antibodies present 0.9925 0.0075 Antibodies absent 0.003 0.997 Suppose that 5% of a large population carries antibodies to HIV in their blood. (a) Draw a tree diagram for selecting a person from this population (outcomes: antibodies present or absent) and for testing his or her blood (outcomes: EIA positive or negative). (Do this on paper. Your instructor may ask you to turn in the work.) (b) What is the probability that the EIA is positive for a randomly chosen person from this population? (c) What is the probability that a person has the antibody given that the EIA test is positive? (This exercise illustrates a fact that is important when considering proposals for widespread testing for HIV, illegal drugs, or agents of biological warfare: if the condition being tested is uncommon in the population, many positives will be false positives.) 8. ?/4 points Notes An insurance company has the following information about drivers aged 16 to 18 years: 25% are involved in accidents each year; 10% in this age group are A students; among those involved in an accident 5% are A students. (a) Let A be the event that a young driver is an A student and C the event that a young driver is involved in an accident this year. State the information given in terms of probabilities and conditional probabilities for the events A and C. P(C) = P(A) = P(A|C) = (b) What is the probability that a randomly chosen young driver is an A student and is involved in an accident? 9. ?/1 points Notes An examination consists of multiple-choice questions, each having five possible answers. Linda estimates that she has probability 0.85 of knowing the answer to any question that may be asked. If she does not know the answer, she will guess, with conditional probability 1/5 of being correct. Find the conditional probability that Linda knows the answer, given that she supplies the correct answer. 10. ?/5 points Notes The first digits of numbers in legitimate records often follow a distribution known as Benford's Law. Here is the distribution. First digit: 1 2 3 4 5 6 7 8 9 Probability: 0.305 0.172 0.125 0.097 0.079 0.067 0.058 0.058 0.039 P(A) = P(first digit is 1) = 0.305 P(B) = P(first digit is 6 or greater) = 0.222 P(C) = P(first digit is odd) = 0.606 We will define event D to be {first digit is less than 4}. Using the union and intersection notation, find the following probabilities. (a) P(D) (b) P(B ? D) (c) P(Dc) (d) P(C ? D) (e) P(B ? C) 11. ?/4 points Notes Gain Communications sells aircraft communications units to both the military and the civilain markets. Next year's sales depend on market conditions that cannot be predicted exactly. Gain follows the modern practice of using probability estimates of sales. The military division estimates its sales as follows. X = units sold 1000 3000 5000 10000 Probability 0.1 0.3 0.4 0.2 The corresponding sales estimates for the civilian division are as follows. Y = units sold 300 500 750 Probability 0.3 0.5 0.2 We have already calculated the following statistics. ?X = 5000 units; ?X2 = 7800000; ?Y = 490 units; ?Z = $11715000, where Z = 2000X + 3500Y (a) Find the variance and standard deviation of the estimated sales Y of Gain's civilian unit, using the distribution and mean given above. variance standard deviation (b) Because the military budget and the civilian economy are not closely linked, Gain is willing to assume that its military and civilian sales vary independently. Combine your result from (a) with the results above to obtain the standard deviation of the total sales X + Y. (c) Find the standard deviation of the estimated profit, Z = 2000X + 3500Y. 12. ?/5 points Notes A mechanical assembly (Figure 7.12) consists of a shaft with a bearing at each end. The total length of the assembly is the sum X + Y + Z of the shaft length X and the lengths Y and Z of the bearings. These lengths may vary from part to part in production, independently of each other and with normal distributions. The shaft length X has mean 11.8 inches and standard deviation of 0.002 inch, while each bearing length Y and Z has a mean 0.4 inch and standard deviation 0.001 inch. (a) According to the 68-95-99.7 rule about 95% of all shafts have lengths in the range 11.8 d1 inches. What is the value of d1? Similarly, about 95% of the bearing lengths fall in the range of 0.4 d2. What is the value of d2? (b) It is a common practice in the industry to state the "natural tolerance" of parts in the form used in part (a). An engineer who know no statistics thinks that tolerances add, so that the natural tolerance for the total length of the assembly (shaft and two bearings) is 12 d inches, where d = d1 + 2 d2. Find the standard deviation of the total length X + Y + Z. Then find the value of d such that about 95% of all assemblies have lengths in the range of 12 d. Was the engineer correct? Yes No 13. ?/4 points Notes You are playing a board game in which the severity of a penalty is determined by rolling three dice and adding the spots on the up-faces. The dice are all balanced so that each face is equally likely, and the three dice fall independently. (a) Give a sample space for the sum X of the spots. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 (b) Find P(X = 6). (c) If X1, X2, and X3 are the number of spots on the up-faces of the three dice, then X = X1 + X2 + X3. Use this fact to find the mean ?X and the standard deviation ?X without finding the distribution of X. (Start with the distribution of each of the Xi.) mean std dev 14. ?/1 points Notes The Tri-State Pick 3 lottery game offes a choicce of several bets. You choose a three-digit number. The lottery commission announces the winning three-digit number, chosen at random, at the end of each day. The "box" pays $82.33 if the number you choose has the same digits as the winning number, in any order. Find the expected payoff for a $1 bet on the box. (Assume that you chose a number having three different digits. Round to the nearest cent.) 15. ?/3 points Notes How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter occupied units in San Jose, California. Rooms 1 2 3 4 5 6 7 8 9 10 Owned 0.003 0.002 0.023 0.111 0.208 0.227 0.189 0.149 0.053 0.035 Rented 0.008 0.027 0.287 0.373 0.168 0.097 0.021 0.013 0.003 0.003 Find the mean number of rooms for both types of housing unit. Owned rooms Rented rooms How do the means reflect the differences between the distributions of these housing types? The value of ? for owned units indicates skewness in that distribution. The value of ? for owned units indicates symmetry in that distribution. The value of ? for owned units indicates randomness in that distribution. The value of ? for rented units indicates skewness in that distribution. The value of ? for rented units indicates symmetry in that distribution. The value of ? for rented units indicates randomness in that distribution. 16. ?/3 points Notes In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. (a) An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimple, ripples, etc.) in the car's paint. Each observation falls into a "success" or "failure." There is a fixed number n of observations. The n observations are all independent. The probability of success p is the same for each observation. None of the binomial conditions are met. (b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty. X is the number who say "Yes." Each observation falls into a "success" or "failure." There is a fixed number n of observations. The n observations are all independent. The probability of success p is the same for each observation. None of the binomial conditions are met. (c) Joe buys a ticket in his state's "Pick 3" lottery game every week; X is the number of times in a year that he wins a prize. Each observation falls into a "success" or "failure." There is a fixed number n of observations. The n observations are all independent. The probability of success p is the same for each observation. None of the binomial conditions are met. 17. ?/5 points Notes For each of the parts below that describe a geometric setting, find the probability that X = 3. (If a geometric setting is not described, enter NONE.) (a) Flip a coin until you observe a tail. (b) Record the number of times a player makes both shots in a one-and-one foul-shooting situation. (In this situation, you get to attempt a second shot only if you make your first shot.) (c) Draw a card from a deck, observe the card, and replace the card within the deck. Count the number of times you draw a card in this manner until you observe a jack. (d) Buy a "Match 6" lottery ticket every day until you win the lottery. (In a "Match 6" lottery, a player chooses 6 different numbers from the set {1, 2, 3,..., 44}. A lottery representative draws 6 different numbers from this set. To win, the player must match all 6 numbers, in any order.) (e) There are 10 red marbles and 5 blue marbles in a jar. You reach in and, without looking, select a marble. You want to know how many marbles you will have to draw (without replacement), on average, in order to be sure that you have 3 red marbles. 18. ?/4 points Notes You operate a restaurant. You read that a sample survey by the National Restaurant Association shows that 30% of adults are committed to eating nutritious food when eating away from home. To help plan your menu, you decide to conduct a sample survey in your own area. You will use random digit dialing to contact an SRS of 220 households by telephone. (a) If the national result holds in your area, is it reasonable to use the binomial distribution with n = 220 and p = 0.30 to describe the count X of respondents who seek nutritious food when eating out? Explain why. Yes; the binomial conditions are not met but the law of large numbers says we can still use this distribution. No; the binomial conditions are met but the sample size is small compared to the population size. No; the binomial conditions are not met and the sample size is small compared to the population size. Yes; the binomial conditions are met and the sample size is small compared to the population size. (b) What is the mean number of nutrition-conscious people in your sample if p = 0.30 is true? What is the standard deviation? (c) What is the probability that X lies between 61 and 71? Make sure that the rule of thumb conditions are satisfied, and then use a normal approximation to answer the question. 19. ?/3 points Notes Suppose that James guesses on each question of a 48-item true-false quiz. Find the probability that James passes if each of the following is true. (a) A score of 24 or more correct is needed to pass. (b) A score of 29 or more correct is needed to pass. (c) A score of 31 or more correct is needed to pass. 20. ?/5 points Notes A federal report finds that lie detector tests given to truthful persons have probability about 0.12 of suggesting that the person is deceptive. (a) A company asks 14 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 14 answer truthfully. What is the probability that the lie detector says all 14 are truthful? What is the probability that the lie detector says at least 1 is deceptive? (b) What is the mean number among 14 truthful persons who will be classified as deceptive? What is the standard deviation of this number? (c) What is the probability that the number classified as deceptive is less than the mean? 21. ?/5 points Notes Investors remember 1987 as the year stocks lost 20% of their value in a single day. For 1987 as a whole, the mean return of all common stocks on the New York Stock Exchange was ? = -4%. (That is, these stocks lost an average of -4%. of their value in 1987.) The standard deviation of returns was about ? = 29%. (a) What are the mean and the standard deviation of the distribution of 6-stock portfolios in 1987. ? = % ? = % (b) Assuming that the population distribution of returns on individual common stocks is normal, what is the probability that a randomly chosen stock showed a return of at least 3% in 1987? (c) Assuming that the population distribution of returns on individual common stocks is normal, what is the probability that a randomly chosen portfolio of 4 stocks showed a return of at least 3% in 1987? (d) What percentage of 4-stock portfolios lost money in 1987? % 22. ?/3 points Notes Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is ? = 11.3 milligrams. Juan repeats the measurement 6 times and records the mean x of his 6 measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 6 measurements and averaging them, what would be the standard deviation of all his x's?) mg. (b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 3.2 milligrams? Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement. The average of several measurements will always have a greater standard deviation than the result of a single measurement. The average of several measurements will always equal the true mean. The average of several measurements is much more likely to be close to the true mean than a single measurement. 23. ?/1 points Notes Sulfur compounds such as dimethyl sulfide (DMS) are sometimes present in wine. DMS causes "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of DMS that the human nose can detect. Different people have different thresholds, so we start by asking about the DMS threshold in the population of all adults. Extensive studies have found that the DMS odor threshold of adults follows roughly a normal distribution with mean ? = 23.8 micrograms per liter and standard deviation ? = 7.4 micrograms per liter. In an experiment, we present tasters with both natural wine and the same wine spiked with DMS at different concentrations to find the lowest concentration at which they identify the spiked wine. Here are the odor thresholds (measured in micrograms of DMS per liter of wine) for 10 randomly chosen subjects. 25 30 25 28 30 34 36 34 36 35 The mean threshold for these subject is x = 31.3. Find the probability of getting a sample mean even farther away from ? than x = 31.3. 24. ?/2 points Notes High school dropouts make up 16% of all Americans aged 18 to 24. A vocational school that wants to attract dropouts mails an advertising flyer to 24850 persons between the ages of 18 and 24. (a) If the mailing list can be considered a random sample of the population, what is the mean number of high school dropouts who will receive the flyer? (b) What is the probability that at least 4098 dropouts will receive the flyer? (Use the normal approximation to the binomial distribution to answer this question. Round your answer to four decimal places.) 25. ?/1 points Notes A national opinion poll recently estimated that 44% ( = 0.44) of all adults agree that parents of school-age children should be given vouchers good for education at any public or private school of their choice. The polling organization used a probability sampling method for which the sample proportion has a normal distribution with standard deviation about 0.015. If a sample were drawn by the same method from the state of New Jersey (population 7.8 million) instead of from the entire United States (population 280 million), would this standard deviation be larger, about the same, or smaller? larger the same smaller,I reset the deadline.,Thank you. How will I receive the answers?,THANK YOU SOOO MUCH!!!
