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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+d. How would the probability of the system working change if a 5–6 subsystem was added in parallel with the other two subsystems?1 2 3 4
=+c. The system won’t work if the 1–2 subsystem doesn’t work and if the 3–4 subsystem also doesn’t work. What is the probability that the system won’t work? that it will work?
=+b. What is the probability that the 1–2 subsystem doesn’t work? that the 3–4 subsystem doesn’t work?
=+a. The 1–2 subsystem works only if both components work. What is the probability of this happening?
=+and that these four outcomes are independent (the four components work independently of one another).
=+6.13 Consider a system consisting of four components, as pictured in the following diagram: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, and P(4 works) 5 .9
=+d. What is the probability that each person wins one match? (Hint: There are two different ways for this to happen. Calculate the probability of each separately, and then add.)
=+c. What is the probability that A loses both her matches?
=+b. What is the probability that A wins both her matches?
=+a. What is the probability that A wins both her matches and that B beats C?
=+5 .8, and P(B beats C) 5 .6 and that the outcomes of the three matches are independent of one another.
=+6.12 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)
=+b. Can you spot the error in the reasoning that leads to the stated probability of 1/144? What effect does this error have on the probability of occurrence? Do you think that 1/144 is larger or smaller than the correct probability of occurrence?
=+a. What reasoning did the expert use to arrive at the probability of 1/144?
=+6.11 The following case study is reported in the article“Parking Tickets and Missing Women,” which appears in an early edition of the book Statistics: A Guide to the Unknown. In a Swedish trial on a charge of overtime parking, a police officer testified that he had noted the position of the
=+c. What is the probability that at least one call results in a reservation being made?
=+b. What assumption did you make in order to calculate the probability in Part (a)?
=+a. Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls results in a reservation?
=+6.10 ▼ Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.
=+c. What is the probability that Jeanie remembers the first errand but not the second or third?
=+b. What is the probability that Jeanie remembers at least one of the three errands?
=+a. What is the probability that Jeanie forgets all three errands? What assumptions did you make to calculate this probability?
=+6.9 Jeanie is a bit forgetful, and if she doesn’t make a “to do” list, the probability that she forgets something she is supposed to do is .1. Tomorrow she intends to run three errands, and she fails to write them on her list.
=+6.7 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%gan used If a rand
=+proportion of all tested kindergartners who were found to have TB was .0006. The corresponding proportion for recent immigrants (thought to be a high-risk group) was.0075. Suppose that a Santa Clara County kindergartner is to be selected at random. Are the outcomes selected student is a recent
=+6.5 The Associated Press (San Luis Obispo TelegramTribune, August 23, 1995) reported on the results of mass screening of schoolchildren for tuberculosis (TB). It was reported that for Santa Clara County, California, the
=+University of Buffalo is quoted as saying, “I’m a bit surprised, but I wouldn’t characterize it as bizarre. It’s randomness. Every number has the same chance of coming up. People tend to read into these things. I’m sure that whatever numbers come up tonight, they will have some
=+6.3 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 U.S. adults. If a U.S. adult is selected at random, are the outcomes selected adult is male and selected
=+f. Do you think it is reasonable to assume that the requests made in successive calls are independent? Explain.
=+e. Still assuming independence, calculate the probability that exactly one of the next two calls will be for medical assistance. (Hint: There are two different possibilities that you should consider. The one call for medical assistance might be the first call, or it might be the second call.)
=+d. Still assuming independence, calculate the probability that for two successive calls, the first is for medical assistance and the second is not for medical assistance.
=+c. Assuming that successive calls are independent of one another (i.e., knowing that one call is for medical assistance doesn’t influence our assessment of the probability that the next call will be for medical assistance), calculate the probability that both of two successive calls will be
=+b. What is the probability that a call is not for medical assistance?
=+6.2 M ical as equipm that an incoming call is for medical assistance is .85.This can be expressed as P(call is for medical assistance)5 .85.
=+b. The research that was the basis for the New York Times article was a study of 2329 consecutive cardiac arrests in New York City. To justify the “1 in 100 chance of survival” statement, how many of the 2329 cardiac arrest sufferers do you think survived?Explai
=+a. Give a relative frequency interpretation of the given probability.
=+(The article attributed this poor survival rate to factors common in large cities: traffic congestion and the difficulty of finding victims in large buildings. Similar studies in smaller cities showed higher survival rates.)
=+6.1 An article in the New York Times (March 2, 1994)reported that people who suffer cardiac arrest in New York City have only a 1 in 100 chance of survival. Using probability notation, an equivalent statement would be P(survival) 5 .01 for people who suffer a cardiac arrest in New York City
=+4.64 ● The article “Can We Really Walk Straight?”(American Journal of Physical Anthropology [1992]: 19–27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target 60 m away at normal speed. Consider the following data on cadence
=+4.63 ● The amount of aluminum contamination (in parts per million) in plastic was determined for a sample of 26 plastic specimens, resulting in the following data (“The Log Normal Distribution for Modeling Quality Data When the Mean Is Near Zero,” Journal of Quality Technology[1990]:
=+4.62 The paper cited in Exercise 4.61 also reported values of single-leg power for a low workload. The sample mean for n 5 13 observations was x 5 119.8 (actually 119.7692), and the 14th observation, somewhat of an outlier, was 159. What is the value of for the entire sample?
=+d. Suppose that the largest observation had been 204 rather than 244. How would the trimmed mean in Part (c)change? What if the largest value had been 284?
=+c. Calculate a trimmed mean by eliminating the smallest and the largest sample observations. What is the corresponding trimming percentage?
=+244. How would the mean and median change?
=+b. Suppose that the first observation had been 204, not
=+a. Calculate and interpret the sample mean and median.
=+4.61 ● The paper “The Pedaling Technique of Elite Endurance Cyclists” (International Journal of Sport Biomechanics [1991]: 29–53) reported the following data on single-leg power at a high workload:244 191 160 187 180 176 174 205 211 183 211 180 194 200
=+Compute the values of the sample mean and median. Why are these values different here? Which one do you regard as more representative of the sample, and why?
=+4.60 ● The risk of developing iron deficiency is especially high during pregnancy. Detecting such a deficiency is complicated by the fact that some methods for determining iron status can be affected by the state of pregnancy itself. Consider the following data on transferrin receptor
=+4.65 ● The article “Comparing the Costs of Major Hotel Franchises” (Real Estate Review [1992]: 46–51) gave the following data on franchise cost as a percentage of total room revenue for chains of three different types:Budget 2.7 2.8 3.8 3.8 4.0 4.1 5.5 5.9 6.7 7.0 7.2 7.2 7.5 7.5 7.7 7.9
=+Construct a boxplot for each type of hotel, and comment on interesting features, similarities, and differences.
=+4.66 ● The accompanying data on milk volume (in grams per day) were taken from the paper “Smoking During Pregnancy and Lactation and Its Effects on Breast Milk Volume” (American Journal of Clinical Nutrition [1991]:1011–1016):Smoking 621 793 593 545 753 655 mothers 895 767 714 598 693
=+d. What percentile corresponds to an exam score of 140?
=+c. What z score is associated with an exam score of 90?
=+b. What is the approximate value of the standard deviation of exam scores?
=+a. What is the 84th percentile?
=+4.69 Suppose that the distribution of scores on an exam is closely described by a normal curve with mean 100. The 16th percentile of this distribution is 80.
=+e. Construct the boxplot for this data set.
=+d. Are there any mild or extreme outliers present in this data set?
=+c. Compute the upper quartile, the lower quartile, and the interquartile range.
=+b. Calculate the 10% trimmed mean. How does the value of the trimmed mean compare to that of the sample mean?Which would you recommend as a measure of location?Explain.
=+a. Calculate the values of the sample mean and the standard deviation.
=+4.68 ● Age at diagnosis for each of 20 patients under treatment for meningitis was given in the paper “Penicillin in the Treatment of Meningitis” (Journal of the American Medical Association [1984]: 1870–1874). The ages (in years) were as follows:18 18 25 19 23 20 69 18 21 18 20 18 18 20
=+4.67 The Los Angeles Times (July 17, 1995) reported that in a sample of 364 lawsuits in which punitive damages were awarded, the sample median damage award was$50,000, and the sample mean was $775,000. What does this suggest about the distribution of values in the sample?
=+c. Draw a modified boxplot, and comment on the interesting features of the plot.
=+b. What is the value of the interquartile range? Are there outliers in this data set?
=+a. Compute the median and the quartiles for this data set.
=+a. Which of the two given values do you think is the mean and which is the median? Explain your reasoning.
=+4.53 The San Luis Obispo Telegram-Tribune (November 29, 1995) reported the values of the mean and median salary for major league baseball players for 1995. The values reported were $1,110,766 and $275,000.
=+c. By how much could the largest time be increased without affecting the value of the sample median? By how much could this value be decreased without affecting the sample median?
=+b. Calculate the values of the sample mean and median.
=+a. Construct a stem-and-leaf display of the data. Will the sample mean or the sample median be larger for this data set?
=+4.52 ● A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (in seconds) to complete the escape (“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,” Ergonomics[1997]: 281–292):389 356 359 363
=+County supervisors are supposed to be paid the average of the two counties among these six in the middle of the salary range. Which measure of center determines this salary, and what is its value? Why is the other measure of center featured in this section not as favorable to these supervisors
=+4.51 The San Luis Obispo Telegram-Tribune (October 1, 1994) reported the following monthly salaries for supervisors from six different counties: $5354 (Kern), $5166(Monterey), $4443 (Santa Cruz), $4129 (Santa Barbara),$2500 (Placer), and $2220 (Merced). San Luis Obispo
=+Five-Number Summaries I II III IV Minimum 40 4 0.0 10 Lower quartile 45 8 0.1 34 Median 71 16 0.9 44 Upper quartile 88 25 2.2 82 Maximum 106 30 5.1 132
=+2. Would an airline have a lower risk of a potentially dangerous situation if th
=+creating a potentially dangerous situation for an airline?
=+1. What role does variability in passenger weights play in
=+b. The reported mean was computed using the salaries of all major league players in 1995. For the 1995 salaries, is the reported mean the population mean m or the sample mean Explain.
=+4.54 Because some homes have selling prices that are much higher than most, the median price is usually used to describe a “typical” home price for a given location.The three accompanying quotes are all from the San Luis Obispo Tribune, but each gives a different interpretation of the median
=+a. “So we have gone from 23 percent to 27 percent of county residents who can afford the median priced home at $278,380 in SLO County. That means that half of the homes in this county cost less than $278,380 and half cost more.” (October 11, 2001)
=+gram per minute) while the participants pedaled at a specified rate on a bicycle ergometer:12.81 14.95 15.83 15.97 17.90 18.27 18.34 19.82 19.94 20.62 20.88 20.93 20.98 20.99 21.15 22.16 22.24 23.16 23.56 35.78 36.73
=+4.59 ● To understand better the effects of exercise and aging on various circulatory functions, the article “Cardiac Output in Male Middle-Aged Runners” (Journal of Sports Medicine [1982]: 17–22) presented data from a study of 21 middle-aged male runners. The following data set gives
=+b. Construct a boxplot, and comment on the important features of the plot.
=+a. Are there any observations that are mild outliers? Extreme outliers?
=+4.58 ● The percentage of juice lost after thawing for 19 different strawberry varieties appeared in the article “Evaluation of Strawberry Cultivars with Different Degrees of Resistance to Red Scale” (Fruit Varieties Journal [1991]:12–17):46 51 44 50 33 46 60 41 55 46 53 53 42 44 50 54 46
=+4.57 For the data of Exercise 4.55, multiply each data value by 10. How does s for the new values compare to s for the original values? More generally, what happens to s if each observation is multiplied by the same positive constant c?
=+4.56 For the data in Exercise 4.55, subtract 10 from each sample observation. For the new set of values, compute the mean and the deviations from the mean. How do these deviations compare to the deviations from the mean for the original sample? How does s 2 for the new values compare to s 2 for
=+b. Compute the sample variance and standard deviation for this data set. Interpret these values.
=+a. Compute the sample mean distance at which the bat first detects an insect.
=+4.55 ● Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper appearing in Animal Behaviour (“The Echolocation of Flying Insects by Bats” [1960]: 141–154) gave the following
=+c. “‘Your median is going to creep up above $300,000 if there is nothing available below $300,000,’ Walker said.”(February 26, 2002)x?
=+b. “The county’s median price rose to $285,170 in the fourth quarter, a 9.6 percent increase from the same period a year ago, the report said. (The median represents the midpoint of a range.)” (February 13, 2002)
=+Assuming that the new estimate of the average passenger weight is accurate, discuss the following questions with a partner and then write a paragraph that answers these questions.
=+a. Would you recommend using the standard deviation or the iqr as a measure of variability for this data set?
=+Thursday, whereas New Year’s Day, July 4th and Christmas do not always fall on the same day of the week every year. Based on the given data, is there more or less variability in the speeding-related crash fatality numbers from year to year for same day of the week holiday periods
=+c. Suppose that it is decided to include 15 more patients in the study. How many of these would have to be S’s to give p5.80 for the entire sample of 25 patients?
=+b. Replace each S with a 1 and each F with a 0. Then calculate for this numerically coded sample. How does compare to p?
=+a. What is the value of the sample proportion of successes?
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