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statistics for experimentert

Questions and Answers of Statistics For Experimentert

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
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
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
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.
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
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
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
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
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
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
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
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)
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
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
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
●● 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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”
6.67 The authors of the paper “Do Physicians Know when Their Diagnoses Are Correct?” (Journal of General Internal Medicine [2005]: 334–339) presented detailed case studies to medical students
6.66 Refer to the information given in the previous exercise about customers of a large cable company.a. Suppose two customers are to be selected at random. Would it be reasonable to consider the
6.65 A large cable company reports the following:● 80% of its customers subscribe to cable TV service● 42% of its customers subscribe to Internet service● 32% of its customers subscribe to
6.64 Blue Cab operates 15% of the taxis in a certain city, and Green Cab operates the other 85%. After a nighttime hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue.
6.63 According to a July 31, 2013, posting on cnn.com, a 2010 study in the journal Pediatrics found that 8%of children younger than age 18 in the United States have at least one food allergy. Among
6.62 Let F denote the event that a randomly selected registered voter in a certain city has signed a petition to recall the mayor. Also, let E denote the event that the randomly selected registered
6.61 There are two traffic lights on the route used by a certain individual to go from home to work. Let E denote the event that the individual must stop at the first light, and define the event F in
6.60 A construction firm bids on two different contracts.Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) 5
6.59 ▼ A certain university has 10 vehicles available for use by faculty and staff. Six of these are vans and four are cars. On a particular day, only two requests for vehicles have been made.
6.58 Refer to the previous exercise. Suppose now that for a probability question, 100 answers are submitted, of which 50 are correct. Calculate the probabilities in Parts (a) and (b) of the previous
6.57 The National Public Radio show Car Talk has a feature called “The Puzzler.” Listeners are asked to send in answers to some puzzling questions—usually about cars but sometimes about
6.56 A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small(S), medium (M), and large (L). The proportions of the two brands and of the three
6.55 A shipment of 5000 printed circuit boards contains 40 that are defective. Two boards will be chosen at random, without replacement. Consider the two events E1 5 event that the first board
6.54 Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) 5 .7 P(A beats C) 5 .8 P(B beats C) 5 .6 and that
6.53 The following case study was reported in the article“Parking Tickets and Missing Women,” which appeared in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial
Components 1 and 2 form a series subsystem, as do Components 3 and 4. The two subsystems are connected in parallel. Suppose that P(1 works) 5 .9 P(2 works) 5 .9 P(3 works) 5 .9 P(4 works) 5 .9 and
6.51 Consider a system consisting of four components, as pictured in the following diagram:1 2 3 4
6.50 ▼ Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.a. Suppose that an operator handles 10 calls. What is the probability that none of the
6.48 In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year.People are selected for jury duty at random from those eligible, and the same individual
6.47 A Gallup survey of 2002 adults found that 46% of women and 37% of men experience pain daily (San Luis Obispo Tribune, April 6, 2000). Suppose that this information is representative of adult
6.46 The article “SUVs Score Low in New Federal Rollover Ratings” (San Luis Obispo Tribune, January 6, 2001)gave information on death rates for various kinds of accidents by vehicle type for
6.45 The report “TV Drama/Comedy Viewers and Health Information” (www.cdc.gov/Healthmarketing) describes the results of a large survey involving approximately 3500 people that was conducted for

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