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##### 1. ?/3 points Notes At a party there are 37 stude...

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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!!!

Paper#9816 | Written in 18-Jul-2015

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