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statistics for experimentert

Questions and Answers of Statistics For Experimentert

7.125 The lightbulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. If length of life is approximately normally distributed with a standard
7.124 Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean pH of 6.00 and a standard deviation of 0.10. If the pH of a randomly selected soil
7.123 Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all
7.122 Refer to the previous exercise, and let y be the number of games won by the series loser. Determine the probability distribution of y.
7.121 Kyle and Lygia are going to play a series of Trivial Pursuit games. The first person to win four games will be declared the winner. Suppose that outcomes of successive games are independent and
7.119 Two sisters, Allison and Teri, have agreed to meet between 1 and 6 p.m. on a particular day. In fact, Allison is equally likely to arrive at exactly 1 p.m., 2 p.m., 3 p.m., 4 p.m., 5 p.m., or 6
7.118 The longest “run” of S’s in the sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh positions. Consider a binomial experiment with n 5 4,
7.117 The Wall Street Journal (February 15, 1972) reported that General Electric was sued in Texas for sex discrimination over a minimum height requirement of 5 ft. 7 in. The suit claimed that this
7.116 A machine producing vitamin E capsules operates so that the actual amount of vitamin E in each capsule is normally distributed with a mean of 5 mg and a standard deviation of 0.05 mg. What is
7.115 The lifetime of a certain brand of battery is normally distributed with a mean value of 6 hours and a standard deviation of 0.8 hours when it is used in a particular DVD player. Suppose that
7.114 The amount of time spent by a statistical consultant with a client at their first meeting is a random variable having a normal distribution with a mean value of 60 minutes and a standard
7.113 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
7.112 A coin is flipped 25 times. Let x be the number of flips that result in heads (H). Consider the following rule for deciding whether or not the coin is fair:Judge the coin fair if 8 # x #
7.111 Suppose that fuel efficiency for a particular model car under specified conditions is normally distributed with a mean value of 30.0 mpg and a standard deviation of 1.2 mpg.a. What is the
7.110 A pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas.Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed
7.109 A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable
7.107 A business has six customer service telephone lines.Let x denote the number of lines in use at a specified time. Suppose that the probability distribution of x is as follows:x 0 1 2 3 4 5 6
7.106 A soft-drink machine dispenses only regular Coke and Diet Coke. Sixty percent of all purchases from this machine are diet drinks. The machine currently has 10 cans of each type. If 15 customers
7.105 Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standard deviation of x are 266 days and 16
4. Combine the observations from your group with those from the other groups. Use the resulting data to approximate the distribution of x. Comment on the resulting distribution in the context of the
3. Suppose that a carton of one dozen eggs does happen to have exactly three eggs that carry salmonella and that the manager does as he proposes: selects three eggs at random and throws them out,
2. Suppose the following argument is made for threeegg quiches rather than four-egg quiches: Let x # number of eggs that carry salmonella. Then p(0) 5 p(x 5 0) 5 (0.75)3 5 .422 for three-egg quiches
1. Working in a group or as a class, discuss the folly of the above statement!
2. Working as a group, each student in your class should flip a coin 30 times and note the number of heads in the 30 tosses. If there are fewer than 50 students in the class, each student should
1. Do you think that any of the three students made up the x values shown in their dotplot? If so, which ones, and what about the dotplot makes you think the student did not actually do the coin
7.104 A company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. Suppose that only 20% of its mufflers are replaced
7.102 Suppose that 65% of all registered voters in a certain area favor a 7-day waiting period before purchase of a handgun. Among 225 randomly selected registered voters, what is the approximate
7.99 Studies have found that women diagnosed with cancer in one breast also sometimes have cancer in the other breast that was not initially detected by mammogram or physical examination (“MRI
7.98 Symptom validity tests (SVTs) are sometimes used to confirm diagnosis of psychiatric disorders. The paper“Developing a Symptom Validity Test for Post-Traumatic Stress Disorder: Application of
7.97 Suppose that x has a binomial distribution with n 5 50 and p 5 .6, so that m 5 np 5 30 and s 5Ïnps12pd 5 3.4641. Approximate the following probabilities using the normal approximation with the
7.96 The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 500 and standard deviation 75. What is the
7.95 Suppose that the distribution of x 5 the number of items produced by an assembly line during an 8-hour shift can be approximated by a normal distribution with mean value 150 and standard
7.94 Let x denote the IQ of an individual selected at random from a certain population. The value of x must be a whole number. Suppose that the distribution of x can be approximated by a normal
7.93 The following figure appeared in the paper “EDTAExtractable Copper, Zinc, and Manganese in Soils of the Canterbury Plains” (New Zealand Journal of Agricultural Research [1984]: 207–217). A
7.92 ● The paper “Temperature and the Northern Distributions of Wintering Birds” (Ecology [1991]:2274–2285) gave the following body masses (in grams) for 50 different bird species:7.7 10.1
7.91 The article “The Distribution of Buying Frequency Rates” (Journal of Marketing Research [1980]: 210–216)reported the results of a 312-year study of toothpaste purchases. The investigators
7.90 ● Example 7.32 examined rainfall data for Minneapolis–St. Paul. The square-root transformation was used to obtain a distribution of values that was more nearly symmetric than the
7.89 ● Consider the following sample of 25 observations on the diameter x (in centimeters) of a disk used in a certain system:16.01 16.08 16.13 15.94 16.05 16.27 15.89 15.84 15.95 16.10 15.92 16.04
7.88 ● Consider the following 10 observations on the lifetime (in hours) for a certain type of power supply: 152.7, 172.0, 172.5, 173.3, 193.0, 204.7, 216.5, 234.9, 262.6, and 422.6. Construct a
7.87 The following normal probability plot was constructed using part of the data appearing in the paper “Trace Metals in Sea Scallops” (Environmental Concentration and Toxicology 19:
7.86 ● Macular degeneration is the most common cause of blindness in people older than 60 years. One variable thought to be related to a type of inflammation associated with this disease is level
7.85 ● Measures of nerve conductivity are used in the diagnosis of certain medical conditions. The paper“Effects of Age, Gender, Height, and Weight on Late Responses and Nerve Conduction Study
7.84 ● The paper “Risk Behavior, Decision Making, and Music Genre in Adolescent Males” (Marshall University, May 2009) examined the effect of type of music playing and performance on a risky,
7.83 ● The authors of the paper “Development of Nutritionally At-Risk Young Children is Predicted by Malaria, Anemia, and Stunting in Pemba, Zanzibar” (The Journal of Nutrition
7.82 ▼ Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboard can be approximated by a normal curve with mean 60 wpm and
7.79 Refer to the previous exercise. Suppose that there are two machines available for cutting corks. The machine described in the preceding problem produces corks with diameters that are
7.78 A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter for the corks produced is well approximated by a normal distribution with mean 3 cm and
7.74 The paper referenced in Example 7.30 (“Estimating Waste Transfer Station Delays Using GPS,” Waste Management [2008]: 1742–1750) describing processing times for garbage trucks also provided
7.73 Emissions of nitrogen oxides, which are major constituents of smog, can be modeled using a normal distribution. Let x denote the amount of this pollutant emitted by a randomly selected vehicle
7.72 Consider babies born in the “normal” range of 37–43 weeks gestational age. The paper referenced in Example 7.27 (“Fetal Growth Parameters and Birth Weight: Their Relationship to Neonatal
7.71 Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean m 5 5 ml and standard deviation s 5 0.2
7.70 Because P(z , .44) 5 .67, 67% of all z values are less than .44, and .44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for
7.69 Determine the value of z* such thata. 2z* and z* separate the middle 95% of all z values from the most extreme 5% (Hint: See Example 7.26.)b. 2z* and z* separate the middle 90% of all z values
7.68 Determine the value z* thata. Separates the largest 3% of all z values from the others (Hint: See Example 7.26.)b. Separates the largest 1% of all z values from the othersc. Separates the
b. P(z , z*) 5 .01c. P(z , z*) 5 .05d. P(z . z*) 5 .02e. P(z . z*) 5 .01f. P(z . z* or z , 2z*) 5 .20
7.67 Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Hint: See Example 7.25.)a. P(z , z*) 5 .025
7.66 Let z denote a random variable having a normal distribution with m 5 0 and s 5 1. Determine each of the following probabilities. (Hint: See Examples 7.27 and 7.28.)a. P(z , 0.10)b. P(z ,
7.62 ▼ The article on polygraph testing of FBI agents referenced in Exercise 7.51 indicated that the probability of a false-positive (a trustworthy person who nonetheless fails the test) is .15.
7.60 Sophie is a dog that loves to play catch. Unfortunately, she isn’t very good, and the probability that she catches a ball is only .1. Let x be the number of tosses required until Sophie
7.59 Suppose a playlist on an MP3 music player consists of 100 songs, of which eight are by a particular artist.Suppose that songs are played by selecting a song at random (with replacement) from the
7.58 Suppose that 90% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample
7.57 A city ordinance requires that a smoke detector be installed in all residential housing. There is concern that too many residences are still without detectors, so a costly inspection program is
7.56 Suppose that 20% of the 10,000 signatures on a certain recall petition are invalid. Would the number of invalid signatures in a sample of 2000 of these signatures have(approximately) a binomial
7.55 You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each question. Suppose that you have not studied and so must guess (select one of the five
7.54 Thirty percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection.a. Among 15 randomly selected cars, what is the probability that at most
7.53 Suppose that the probability is .1 that any given citrus tree will show measurable damage when the temperature falls to 308F. (Hint: See Example 7.21.)a. If the temperature does drop to 308F,
7.52 Industrial quality control programs often include inspection of incoming materials from suppliers.If parts are purchased in large lots, a typical plan might be to select 20 parts at random from
7.51 The article “FBI Says Fewer than 25 Failed Polygraph Test” (San Luis Obispo Tribune, July 29, 2001) states that false-positives in polygraph tests (tests in which an individual fails even
7.48 Example 7.18 described a study in which a person was asked to determine which of three t-shirts had been worn by her roommate by smelling the shirts (“Sociochemosensory and Emotional
7.47 Twenty-five percent of the customers of a grocery store use an express checkout. Consider five randomly selected customers, and let x denote the number among the five who use the express
7.46 Refer to the previous exercise, and suppose that 10 rather than six passengers are selected (n 5 10, p 5 .8). (Hint: Use technology or Appendix Table 9.)a. What is p(8)?b. Calculate P(x # 7).c.
7.45 ▼ The Los Angeles Times (December 13, 1992) reported that what airline passengers like to do most on long flights is rest or sleep. In a survey of 3697 passengers, almost 80% did so. Suppose
7.44 The article “Should You Report That Fender-Bender?”(Consumer Reports, 2013:15) reported that 7 in 10 auto accidents involve a single vehicle. Suppose 15 accidents are randomly selected.
7.43 NBC News reported that 1 in 20 children in the U.S. has a food allergy (May 2, 2013). Consider selecting 10 children at random. Define the random variable x as x 5 number of children in the
7.42 The states of Ohio, Iowa, and Idaho are often confused, probably because the names sound so similar.Each year, the State Tourism Directors of these three states drive to a meeting in one of the
7.41 Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die.a. The probability
7.40 A multiple-choice exam consists of 50 questions.Each question has five choices, of which only one is correct. Suppose that the total score on the exam is computed as y  x1 2 14 x2 where x1 5
7.39 ▼ To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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 
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
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
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
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

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