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statistics for experimentert
Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions
7.38 An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space. Let x 5 the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution:x 13.5 15.9 19.1 p(x) .2
7.37 A grocery store has an express line for customers purchasing five or fewer items. Let x be the number of items purchased by a randomly selected customer using this line. Give examples of two different assignments of probabilities such that the resulting distributions have the same mean but
7.36 An author has written a book and submitted it to a publisher. The publisher offers to print the book and gives the author the choice between a flat payment of $10,000 and a royalty plan. Under the royalty plan the author would receive $1 for each copy of the book sold. The author thinks that
7.35 A local television station sells 15-second, 30-second, and 60-second advertising spots. Let x denote the length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by the following table:x 15 30 60 p(x) .1 .3 .6a. Find the
7.34 Suppose that for a given computer salesperson, the probability distribution of x 5 the number of systems sold in 1 month is given by the following table:x 1 2 3 4 5 6 7 8 p(x) .05 .10 .12 .30 .30 .11 .01 .01a. Find the mean value of x (the mean number of systems sold).b. Find the variance and
7.33 Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is$10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses
7.32 Example 7.11 gave the probability distributions of x 5 number of flaws in a randomly selected glass panel for two suppliers of glass used in the manufacture of flat screen TVs. If the manufacturer wanted to select a single supplier for glass panels, which of these two suppliers would you
7.31 Exercise 7.8 gave the following probability distribution for x 5 the number of courses for which a randomly selected student at a certain university is registered:x 1 2 3 4 5 6 7 p(x) .02 .03 .09 .25 .40 .16 .05 It can be easily verified that m 5 4.66 and s 5 1.20.a. Because m 2 s 5 3.46, the
7.30 Referring to the previous exercise, use the result of Part (a) along with the fact that a carton contains 12 eggs to determine the mean value of z 5 the number of unbroken eggs. (Hint: z can be written as a linear function of y; see Example 7.15.)
7.29 Consider the following probability distribution for y 5 the number of broken eggs in a carton:y 0 1 2 3 4 p(y) .65 .20 .10 .04 .01a. Calculate and interpret my.b. In the long run, for what percentage of cartons is the number of broken eggs less than my? Does this surprise you?c. Why doesn’t
7.28 The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table:x 0 1 2 3 4 p(x) .54 .16 .06 .04 .20a. Calculate the mean value of x.b. What is the probability that x exceeds its mean
7.27 Consider selecting a household in rural Thailand at random. Define the random variable x to be x 5 number of individuals living in the selected household Based on information in an article that appeared in the Journal of Applied Probability (2011: 173–188), the probability distribution
3. Figure 7.10(c) shows three continuous distributions with different means and standard deviations. Which of the three distributions has the largest mean? Which has a mean of about 5? Which distribution has the smallest standard deviation?
2. Figure 7.10(b) shows two continuous probability distributions that have the same mean but different standard deviations. Which distribution—(i) or (ii)—has the larger standard deviation?
1. Figure 7.10(a) shows two discrete probability distributions with the same standard deviation (spread) but different means (center). One distribution has a mean of mx 5 6 and the other has mx 5 10. Which has the mean of 6 and which has the mean of 10?
7.26 Referring to the previous exercise, let x and y be waiting times on two independently selected days.Define a new random variable w by w 5 x 1 y the sum of the two waiting times. The set of possible values for w is the interval from 0 to 40 (because both x and y can range from 0 to 20). It can
7.25 Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the density curve is as pictured (a uniform distribution):0.05 0 20 Minutes Density xa. What is the probability that x is less than 10 minutes? more than 15 minutes?b.
7.24 Let x denote the amount of gravel sold (in tons)during a randomly selected week at a particular sales facility. Suppose that the density curve has height f(x)above the value x, where f sxd 52s1 2 xd 0 # x # 1 0 otherwise The density curve (the graph of f(x)) is shown in the following
7.23 The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research[1984]: 1169– 1174) suggests the uniform distribution on the interval from 7.5 to 20 as a model for x 5 depth (in centimeters) of the bioturbation layer in sediment for a certain
7.22 Refer to the probability distribution given in the previous exercise. Put the following probabilities in order, from smallest to largest:Ps2 , x , 3d, Ps2 # x # 3d, Psx , 2d, Psx . 7d Explain your reasoning.
7.21 A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes)that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density curve is shown in the following figure:1 10
7.20 Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. The density curve of x is as pictured:0 25 50 Shade the area under the curve corresponding to each of the following probabilities (draw a new curve for each part). (Hint: See Example 7.8.)a. Ps10
7.19 A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday’s mail. In actuality, each one could arrive on Wednesday (W), Thursday (T), Friday (F), or Saturday (S). Suppose that the two magazines arrive independently of one another and that
7.18 A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project)in applying for a building permit. Let y be the number of forms required of the next applicant. The probability that y forms are required is known to be
7.17 Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of all such components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested
7.16 A box contains five slips of paper, marked $1, $1, $1,$10, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w 5 amount awarded. Determine the probability distribution of w.
7.15 Suppose that 20% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.a. Find the probability distribution of x. (Hint: Let S denote a
7.14 Of all airline flight requests received by a certain discount ticket broker, 70% are for domestic travel (D)and 30% are for international flights (I). Let x be the number of requests among the next three requests received that are for domestic flights. Assuming independence of successive
7.13 Simulate the chance experiment described in the previous exercise using five slips of paper, with two marked defective and three marked nondefective. Place the slips in a box, mix them well, and draw out two.Record the number of defective boards. Replace the slips and repeat until you have 50
7.12 Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1,2) represents the selection of Boards 1 and 2 for inspection.a.
7.11 Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations.Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the probability distribution of x is given in the following table:x 95
7.10 Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. They report the following information for last year’s graduates:Size of donation $0 $10 $25 $50 Proportion of calls 0.45 0.30 0.20 0.05 Three attempts were made to contact each
7.9 ▼ Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows:y 0 1 2 3 4 p(y) .65 .20 .10 .04 ?a. Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the
7.8 Let x be the number of courses for which a randomly selected student at a certain university is registered.The probability distribution of x appears in the following table:x 1 2 3 4 5 6 7 p(x) .02 .03 .09 .25 .40 .16 .05a. What is P(x 5 4)?b. What is P(x # 4)?c. What is the probability that the
7.7 A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement.List the possible values for each of the following random variables:a. x 5 sum of the two numbersb. y 5 difference between the first and second numbersc. z 5 number of slips selected that show
7.4 A point is randomly selected from the interior of the square pictured.Let x denote the distance from the lower left-hand corner A of the square to the selected point.a. What are possible values of x?b. Is x a discrete or a continuous variable? (Hint: See Example 7.3.)
7.3 Starting at a particular time, each car entering an intersection is observed to see whether it turns left (L) or right (R) or goes straight ahead (S). The experiment terminates as soon as a car is observed to go straight. Let y denote the number of cars observed.a. What are possible y values?b.
●● construct and interpret a normal probability plot.
●● find an area under a normal curve and interpret this area as a probability.
●● compute probabilities involving continuous random variables whose density curves have a simple form.
●● compute and interpret binomial probabilities.
●● distinguish between binomial and geometric random variables.
●● compute and interpret the mean and standard deviation of a discrete random variable.
●● construct the probability distribution of a discrete random variable.
●● distinguish between discrete and continuous random variables.
●● that areas under a density curve for a continuous random variable are interpreted as probabilities.Students will be able to:
●● that a probability distribution describes the long-run behavior of a random variable.
6.103 A transmitter is sending a message using a binary code (a sequence of 0’s and 1’s). Each transmitted bit(0 or 1) must pass through three relays to reach the receiver. At each relay, the probability is .20 that the bit sent on is different from the bit received (a reversal).Assume that the
6.102 Return to Exercise 6.101, and suppose that 4 bulbs are randomly selected from the 25.a. What is the probability that all 4 are good?b. What is the probability that at least 1 selected bulb is bad?
6.101 Suppose that a box contains 25 light bulbs, of which 20 are good and the other 5 are defective. Consider randomly selecting three bulbs without replacement. Let E denote the event that the first bulb selected is good, F be the event that the second bulb is good, and G represent the event that
6.100 Refer to Exercise 6.99, but now suppose that two viewers are randomly selected (without replacement).Let R1 and R2 denote the events that the first and second individuals, respectively, watched an R-rated movie. Are R1 and R2 independent events? Explain.From a practical point of view, can
6.99 A theater complex is currently showing four R-rated movies, three PG-13 movies, two PG movies, and one G movie. The following table gives the number of people at the first showing of each movie on a certain Saturday:Theater Rating Number of Viewers 1 R 600 2 PG-13 420 3 PG-13 323 4 R 196 5 G
6.98 The general addition rule for three events states that PsA or B or Cd 5 PsAd 1 PsBd 1 PsCd 2PsA and Bd 2 PsA and Cd 2PsB and Cd 1 PsA and B and Cd A new magazine publishes columns entitled “Art” (A),“Books” (B), and “Cinema” (C). Suppose that 14% of all subscribers read A 23% read
6.97 There are five faculty members in a certain academic department. These individuals have 3, 6, 7, 10, and 14 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a
6.96 In a school machine shop, 60% of all machine breakdowns occur on lathes and 15% occur on drill presses. Let E denote the event that the next machine breakdown is on a lathe, and let F denote the event that a drill press is the next machine to break down.With PsEd 5 .60 and PsFd 5 .15,
6.95 A single-elimination tournament with four players is to be held. In Game 1, the players seeded (rated) first and fourth play. In Game 2, the players seeded second and third play. In Game 3, the winners of Games 1 and 2 play, with the winner of Game 3 declared the tournament winner. Suppose
6.94 Two individuals, A and B, are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins game) 5 .3, P(B wins game) 5 .2, and P(draw) 5 .5.
6.93 Return to the context of the previous exercise and suppose that 50% of the overnight parcels are sent by means of express mail service A2 and the remaining 10% are sent by means of A3. Of those sent by means of A2, only 1% arrived late, whereas 5% of the parcels handled by A3 arrived late.a.
6.92 A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 2% arrive after the guaranteed delivery time.What is the probability that a randomly selected overnight parcel was shipped by mail service A1 and was late?
6.91 The Australian newspaper The Mercury (May 30, 1995)reported that, based on a survey of 600 reformed and current smokers, 11.3% of those who had attempted to quit smoking in the previous 2 years had used a nicotine aid (such as a nicotine patch). It also reported that 62% of those who quit
6.90 The Associated Press (San Luis Obispo Telegram-Tribune, August 23, 1995) reported on the results of mass screening of schoolchildren for tuberculosis(TB). For Santa Clara County, California, the proportion of all tested kindergartners who were found to have TB was .0006. The corresponding
6.89 Online chat rooms allow people from all over the world to exchange opinions on various topics of interest.A side effect of such conversations is “flaming,”which is negative criticism of others’ contributions to the conversation. The paper “Criticism on the Internet:An Analysis of
6.88 Consider the following information about passengers on a cruise ship on vacation: 40% check work e-mail, 30% use a cell phone to stay connected to work, 25% bring a laptop with them on vacation, 23% both check work e-mail and use a cell phone to stay connected, and 51% neither check work
6.87 A company uses three different assembly lines—A1, A2, and A3—to manufacture a particular component.Of those manufactured by A1, 5% need rework to remedy a defect, whereas 8% of A2’s components and 10% of A3’s components need rework. Suppose that 50% of all components are produced by
7. Do you think that the assumption that the outcomes of successive free throws are independent is reasonable?Explain. (This is a hotly debated topic among both sports fans and statisticians!)
6. Using basic probability rules, we can calculate the probability that a player of this skill level is successful on the next 5 free throw attempts:PsSSSSSd 5 11 2211 2211 2211 2211 22 5 11 225 5 .031 which is relatively small. At first this might seem inconsistent with your answer in Step 5, but
5. Use the combined class data to estimate the probability that a player of this skill level has a streak of at least 5 somewhere in a sequence of 50 free throw attempts.
4. Based on the graph from Step 3, does it appear likely that a player of this skill level would have a streak of 5 or more successes sometime during a sequence of 50 free throw attempts? Justify your answer based on the graph from Step 3.
3. Combine your longest streak value with those from the rest of the class and construct a histogram or dotplot of these longest streak values.
2. For your sequence of 50 tosses, identify the longest streak by looking for the longest string of heads in your sequence. Determine the length of this longest streak.
1. Begin by simulating a sequence of 50 free throws for this player. Because this player has probability of success of .5 for each attempt and the attempts are independent, we can model a free throw by tossing a coin. Using heads to represent a successful free throw and tails to represent a missed
4. Working with a partner, write a paragraph explaining why European sports fans should or should not be worried by the results of the Polish experiment.Your explanation should be based on the observed proportion of heads from the Polish experiment and the graphical display constructed in Step 3.
3. Form a data set that consists of the values for proportion of heads observed in 250 tosses of a fair coin for the entire class. Summarize this data set by constructing a graphical display.
2. For your sequence of 250 tosses, calculate the proportion of heads observed.
1. For this first step, you can either (a) flip a U.S.penny 250 times, keeping a tally of the number of heads and tails observed (this won’t take as long as you think), or (b) simulate 250 coin tosses by using your calculator or a statistics software package to generate random numbers (if you
6.86 Refer to Exercises 6.84 and 6.85. Suppose that the probabilities of timely completion are as in Exercise 6.84 for Maria, Alex, and Juan, but that Jacob has a probability of completing on time of .7 if Juan is on time and .5 if Juan is late.a. Use simulation (with at least 20 trials) to
4. If Juan completes his part on time, the probability that Jacob completes on time is .9, but if Juan is late, the probability that Jacob completes on time is only .7.Use simulation (with at least 20 trials) to estimate the probability that the project is completed on time.Think carefully about
3. If Alex completes his part on time, the probability that Juan completes on time is .8, but if Alex is late, the probability that Juan completes on time is only .5.
2. If Maria completes her part on time, the probability that Alex completes on time is .9, but if Maria is late, the probability that Alex completes on time is only .6.
1. The probability that Maria completes her part on time is .8.
6.84 Four students must work together on a group project.They decide that each will take responsibility for a particular part of the project, as follows:Person Maria Alex Juan Jacob Task Survey design Data collection Analysis Report writing Because of the way the tasks have been divided, one
6.83 Many cities regulate the number of taxi licenses, and there is a great deal of competition for both new and existing licenses. Suppose that a city has decided to sell 10 new licenses for $25,000 each. A lottery will be held to determine who gets the licenses, and no one may request more than
4. Use the simulation results to estimate the desired probabilities.a. Estimate the probability that more than five pairs must be treated before a conclusion can be reached.(Hint: P(more than 5) 5 1 2 P(5 or fewer).)b. Estimate the probability that the researchers will incorrectly conclude that
3. Repeat this whole process until you have results for at least 20 trials (more is better).
2. Continue to select pairs, keeping track of the total number of successes for each treatment. Stop the trial as soon as the number of successes for one treatment exceeds that for the other by 2. This would complete one trial.
1. Use a pair of random digits to simulate one pair of subjects. Let the first digit represent Treatment 1 and use 1–7 as an indication of a success and 8, 9, and 0 to indicate a failure. Let the second digit represent Treatment 2, with 1–4 representing a success. For example, if the two digits
6.82 A medical research team wishes to evaluate two different treatments for a disease. Subjects are selected two at a time, and then one of the pair is assigned to each of the two treatments. The treatments are applied, and each is either a success (S) or a failure (F).The researchers keep track
6.81 On April 1, 2010, the Bureau of the Census in the United States attempted to count every U.S. resident.Suppose that the counts in the table for Exercise 6.81 at the top of the next page are obtained for four counties in one region.a. If one person is selected at random from this region, what
6.80 ▼ The table for Exercise 6.80 at the bottom of the page describes (approximately) the distribution of students by gender and college at a mid-sized public university in the West. Suppose that we will randomly select one student from this university:a. What is the probability that the
6.79 Five hundred first-year students at a state university were classified according to both high school GPA and whether they were on academic probation at the end of their first semester. The data are summarized in the accompanying table.Probation High School GPA 2.5 to,3.0 3.0 to,3.5 3.5 and
6.78 The Los Angeles Times (June 14, 1995) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. The Price Waterhouse accounting firm conducted an independent audit by seeding the mail with letters and recording on-time delivery
6.77 Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of .001).Of those who have the disease, 95% test positive when a certain diagnostic test is applied. Of those who do not have the disease, 90% test negative when the test is applied. Suppose that
6.75 In an article that appears on the web site of the American Statistical Association (www.amstat.org), Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statistics in his work as an attorney. He states:I personally have used statistics in trying to challenge the
6.74 The paper referenced in the previous exercise also included data for a second radiologist, Radiologist 2.Based on the data from the previous exercise for Radiologist 1 and the data in the accompanying table for Radiologist 2, write a paragraph comparing the accuracy of gender predictions made
6.73 Radiologists are often asked to predict the gender of a baby from ultrasound images made during pregnancy.The authors of the paper “The Use of Three-Dimensional Ultrasound for Fetal Gender Determination in the First Trimester” (The British Journal of Radiology,[2003]: 448–451) followed
6.72 The article “Checks Halt over 200,000 Gun Sales”(San Luis Obispo Tribune, June 5, 2000) reported that required background checks blocked 204,000 gun sales in 1999. The article also indicated that state and local police reject a higher percentage of would-be gun buyers than does the FBI,
6.71 Suppose that we define the following events:C 5 event that a randomly selected driver is observed to be using a cell phone A 5 event that a randomly selected driver is observed driving a passenger automobile V 5 event that a randomly selected driver is observed driving a van or SUV T 5 event
6.70 The accompanying table summarizes data from a medical expenditures survey carried out by the National Center for Health Statistics (“Assessing the Effects of Race and Ethnicity on Use of Complementary and Alternative Therapies in the USA,” Ethnicity and Health [2005]: 19–32).Use of
6.69 The report “Twitter in Higher Education: Usage Habits and Trends of Today’s College Faculty” (Magna Publications, September 2009) describes results of a survey of nearly 2000 college faculty. The report indicates the following:● 30.7% reported that they use Twitter and 69.3%said that
6.68 A study of how people are using online services for medical consulting is described in the paper“Internet Based Consultation to Transfer Knowledge for Patients Requiring Specialized Care” (British Medical Journal [2003]: 696–699). Patients using a particular online site could request any
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