The light bulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. If lifetime is approximately normally distributed with a standard deviation of 50 hours, how often should all the bulbs be replaced so that no more than 20% of the bulbs will have already burned out?
> 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 of a substance called soluble Fas Ligand (sFasL) in the blood. Th
> The following normal probability plot was constructed using data on the price of seven 2015 Honda Accords with automatic transmissions that were listed for sale within 25 miles of the zip code 19383 (www.autotrader.com, search conducted on September 24,
> Example 6.14 gave the probability distributions shown below for x = number of flaws in a randomly selected glass panel from Supplier 1 y = number of flaws in a randomly selected glass panel from Supplier 2 for two suppliers of glass used in the manufac
> Consider the variable x = time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of x is well approximated by a normal curve with mean 45 minutes and s
> The paper referenced in the previous exercise also included data on left atrial diameter for children who were considered overweight. For these children, left atrial diameter was approximately normally distributed with a mean of 28 mm and a standard devi
> The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper “left Atrial Size increases with body mass index in children” (Internatio
> 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: a. Calculate the mean value of x. b. Interpret the mean value of x in the conte
> A company receives light bulbs from two different suppliers. Define the variables x and y as x = lifetime of a bulb from Supplier 1 y = lifetime of a bulb from Supplier 2 Five hundred bulbs from each supplier are tested, and the lifetime of each bulb
> 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 = x + y, the sum of the two waiting times. The set of possible values for w is the interval from 0 to 40 (because bot
> Let x be the amount of time (in minutes) that a particular San Francisco commuter will have to wait for a BART train. Suppose that the density curve is as pictured (a uniform distribution): a. What is the probability that x is less than 10 minutes? More
> Suppose that the random variable x = actual weight (in ounces) of a randomly selected package of cereal has the probability distribution described by the density curve pictured here. a. What probability is represented by the shaded area? b. Suppose the
> Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the random variable x as x = the number of people who actually show up for a sold-out flight on this plane From past experience, the
> 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 = amount awarded. Determine
> A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let x be the depth of the lake at the randomly chosen point. What are possible values of x? Is x discrete or continuous?
> 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 evaluation of the contralateral breast in women with recently diag
> A symptom validity test (SVT) is sometimes used to confirm diagnosis of psychiatric disorders. The paper “developing a Symptom validity test for Posttraumatic Stress disorder: Application of the binomial distribution” (Journal of Anxiety Disorders [2008]
> A company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. Only 20% of its mufflers are replaced under this warranty. a. In a random sample of 400 purchases, what is the
> Suppose that 25% of the fire alarms in a large city are false alarms. Let x denote the number of false alarms in a random sample of 100 alarms. Approximate the following probabilities: a. P(20 ≤ x ≤ 30) b. P(20 < x < 30) c. P(x ≥ 35) d. The probabili
> The distribution of 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 deviation 10. a. What is the approximate probability that the number of items produc
> Suppose that 65% of all registered voters in a certain area favor a seven-day waiting period before purchase of a handgun. Among 225 randomly selected registered voters, what is the approximate probability that a. At least 150 favor such a waiting perio
> Seventy percent of the bicycles sold by a certain store are mountain bikes. Among 100 randomly selected bike purchases, what is the approximate probability that a. At most 75 are mountain bikes? b. Between 60 and 75 (inclusive) are mountain bikes? c.
> 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 distribution with mean value 100 and standard deviation 15. Appro
> The longest “run” of S’s in the 10-trial sequence SSFSSSSFFS has length 4, corresponding to the S’s on the fourth, fifth, sixth, and seventh trials. Consider a binomial experiment with n = 4, and let y be the length (number of trials) in the longest run
> 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: In this section, you will see how probabilities for some discrete random variables can be approxi
> 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 want to purchase drinks before the machine is restocked, wha
> 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 size 2000 have (approximately) a binomial distribution? Explain.
> 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 (randomly select one of the five answers) on each question. Let x represent the number o
> A breeder of show dogs is interested in the number of female puppies in a litter. If a birth is equally likely to result in a male or a female puppy, give the probability distribution of the variable x = number of female puppies in a litter of size 5.
> An experiment was conducted to investigate whether a graphologist (a handwriting analyst) could distinguish a normal person’s handwriting from that of a psychotic. A wellknown expert was given 10 files, each containing handwriting samples from a normal p
> Suppose that 5% of cereal boxes contain a prize and the other 95% contain the message, “Sorry, try again.” Consider the random variable x, where x 5 number of boxes purchased until a prize is found. a. What is the probability that at most two boxes must
> Sophie is a dog who loves to play catch. Unfortunately, she isn’t very good at this, and the probability that she catches a ball is only 0.1. Let x be the number of tosses required until Sophie catches a ball. a. Does x have a binomial or a geometric di
> 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 5 fail the inspection? b. Among 15 randomly selected cars
> Refer to the previous exercise, and suppose that 10 rather than 6 passengers are selected (n = 10, p = 0.8). Use Appendix A Table 9 to find the following: a. p(8) b. P(x ≤ 7) c. The probability that more than half of the selected passengers travel wit
> FlightView surveyed 2600 North American airline passengers and reported that approximately 80% said that they carry a smartphone when they travel (www.flightview.com /travelersSurvey/downloads/survey_infographic_poster.pdf, retrieved may 2, 2017). Suppos
> Information Security Buzz provides news for the information security community. In an article published on September 24, 2016, it reported that based on a large international survey of Internet users, 60% of Internet users have installed security solutio
> Women’s Health Magazine surveyed 1187 readers to find out how often people wash their sheets (march 26, 2015, www.womenshealthmag.com/health/dirty-sheets, retrieved may 2, 2017). They found that even though microbiologists recommend that you wash your sh
> Suppose a playlist on an MP3 music player consisting of 100 songs includes 8 by a particular artist. Suppose that songs are played by selecting a song at random (with replacement) from the playlist. The random variable x represents the number of songs un
> 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 a lot and inspect them. Suppose that a lot is judged accept
> 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 checkout. a. Calculate p(2), that is, P(x = 2). b. Calculate P(x
> Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the number among four randomly selected households that have cable TV. Then x is a binomial random variable with n = 4 and p = 0.9. a. Calculate p(2) = P(x =
> Example 6.27 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 (“Socio chemosensory and emotional Functions,” Psychological Science [2009]: 1118– 1123). Suppose that in
> Consider the following sample of 25 observations on x = diameter (in centimeters) of CD disks produced by a particular manufacturer: The 13 largest normal scores for a sample of size 25 are 1.964, 1.519, 1.259, 1.064, 0.903, 0.763, 0.636, 0.519, 0.408,
> The accompanying data on x 5 student-teacher ratio is for a random sample of 20 high schools in Maine selected from a population of 85 high schools. The data are consistent with summary values for the state of Maine that appeared in an article in the Ban
> An automobile manufacturer is interested in the fuel efficiency of a proposed new car design. Six nonprofessional drivers were selected, and each one drove a prototype of the new car from Phoenix to Los Angeles. The resulting fuel efficiencies (x, in mil
> Fat contents (x, in grams) for seven randomly selected hot dog brands that were rated as very good by consumer reports (www.consumerreports.org) are shown below. The normal scores for a sample of size 7 are a. Construct a normal probability plot for the
> Consider the following 10 observations on the lifetime (in hours) for a certain type of power supply: Construct a normal probability plot, and comment on whether it is reasonable to think that the distribution of power supply lifetime is approximately n
> 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, decision-making task. a. Partici
> 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 [2009]: 763–772) studied facto
> Let x denote the duration of a randomly selected pregnancy (the time elapsed between conception and birth). Accepted values for the mean value and standards deviation of x are 266 days and 16 days, respectively. Suppose that the probability distribution
> Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean of 6.00 and a standard deviation of 0.10. Suppose the pH of a randomly selected soil sample from this region will be determined. a. What is th
> 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 scores have been designated A’s. Your score is 89. Did you earn
> 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 feet, 7 inches. The suit claimed that this restriction eliminated more than 94% of adult females fr
> 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 the probability that a randomly selected capsule contains less
> When used in a particular DVD player, 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 hour. Suppose that two new batteries are independently selected and put into the player.
> Suppose that the amount of time spent by a statistical consultant with a client at their first meeting is a random variable that has a normal distribution with a mean value of 60 minutes and a standard deviation of 10 minutes. a. What is the probability
> Suppose that fuel efficiency (miles per gallon, mpg) for a particular car model 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 probability that the fuel efficiency for
> A pizza company advertises that it puts 0.5 pound of real mozzarella cheese on its medium-sized pizzas. In fact, the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pound and a standard deviation of
> The number of vehicles leaving a highway at a certain exit during a particular time period has a distribution that is approximately normal with mean value 500 and standard deviation 75. What is the probability that the number of cars exiting during this
> The paper referenced in Example 6.24 (“estimating waste transfer Station delays using gPS,” Waste Management [2008]: 1742–1750) describing processing times for garbage trucks also provided information on processing times at a second facility. At this sec
> A machine that produces ball bearings has initially been set so that the mean diameter of the bearings it produces is 0.500 inches. A bearing is acceptable if its diameter is within 0.004 inches of this target value. Suppose, however, that the setting ha
> The paper “examining communication- and mediabased recreational Sedentary behaviors Among canadian youth: results from the comPASS Study” (Preventive Medicine [2015]: 74–80) estimated that the time spent playing video or computer games by high school boy
> The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean of 120 seconds and a standard deviation of 20 seconds. The fastest 10% are to be given adv
> The paper referenced in Example 6.21 suggested that a normal distribution with mean 3500 grams and standard deviation 550 grams is a reasonable model for birth weights of babies born in Canada. a. One common medical definition of a large baby is any bab
> Purchases made at small “corner stores” were studied by the authors of the paper “changes in Quantity, Spending, and nutritional characteristics of Adult, Adolescent and child urban corner Store Purchases After an environmental intervention” (Preventive
> The article “new york city’s graffiti-removal response time rises” (The Wall Street Journal, September 16, 2016, www.wsj.com/articles/new-york-citys-graffiti-removal -response-time-rises-1473287392, retrieved may 1, 2017) states that the city took an ave
> Let z denote a random variable having a normal distribution with µ = 0 and σ = 1. Determine each of the following probabilities: a. P(z < 0.10) b. P(z < 20.10) c. P(0.40 < z < 0.85) d. P(20.85 < z < 20.40) e. P(20.40 < z < 0.85) f. P(z > 21.25) g.
> Determine each of the following areas under the standard normal (z) curve: a. To the left of -1.28 b. To the right of 1.28 c. Between -1 and 2 d. To the right of 0 e. To the right of -5 f. Between -1.6 and 2.5 g. To the left of 0.23
> 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 approximately normally distributed with mean 3 cm and standard deviatio
> A machine that cuts corks for wine bottles operates in such a way that the distribution of the diameter of the corks produced is well approximated by a normal distribution with mean 3 cm and standard deviation 0.1 cm. The specifications call for corks wi
> 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 standard deviation 15 wpm (“the effects of Split Keyboard geomet
> Consider the population of all one-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean u = 5 ml and standard deviation σ = 0.2 ml is a reasonable model for the distribution of the varia
> Let z denote a random variable that has a standard normal distribution. Determine each of the following probabilities: a. P(z < 2.36) b. P(z ≤ 2.36) c. P(z < 21.23) d. P(1.14 < z , 3.35) e. P(20.77 ≤ z ≤ 20.55) f. P(z > 2) g. P(z ≥ 23.38) h. P(z <
> A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested in order to
> The article “Kids Digital Day: Almost 8 Hours” (USA TODAY, January 20, 2010) summarized a national survey of 2002 Americans age 8 to 18. The sample was selected to be representative of Americans in this age group. a. Of those surveyed, 1321 reported own
> For the study described in the previous exercise, use the fivestep process for estimation problems (EMC3) to construct and interpret a 90% confidence interval for the proportion of adult American Internet users who use Facebook. Identify each of the five
> The study “The Demographics of Social Media Users” (Pew Research Center, August 19, 2015) reported that 72% of adult American Internet users use Facebook. The 72% figure was based on a representative sample of n = 1602 adult American Internet users. Supp
> Based on data from a survey of 1200 randomly selected Facebook users (USA TODAY, March 24, 2010), a 90% confidence interval for the proportion of all Facebook users who say it is not OK to “friend” someone who reports to you at work is (0.60, 0.64). What
> Describe how each of the following factors affects the width of the large-sample confidence interval for p: a. The confidence level b. The sample size c. The value of pˆ
> Suppose that county planners are interested in learning about the proportion of county residents who would pay a fee for a curbside recycling service if the county were to offer this service. Two different people independently selected random samples of
> In a survey on supernatural experiences, 722 of 4013 adult Americans reported that they had seen a ghost (“What Supernatural Experiences We’ve Had,” USA TODAY, February 8, 2010). Assume that this sample is representative of the population of adult Americ
> Consider taking a random sample from a population with p = 0.25. a. What is the standard error of p ˆ for random samples of size 400? b. Would the standard error of pˆ be smaller for random samples of size 200 or samples of size 400? c. Does cutting t
> In response to budget cuts, county officials are interested in learning about the proportion of county residents who favor closure of a county park rather than closure of a county library. In a random sample of 500 county residents, 198 favored closure o
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who are registered to vote. For which of the following situations
> Will pˆ from a random sample of size 400 tend to be closer to the actual value of the population proportion when p = 0.4 or when p = 0.7? Provide an explanation for your choice.
> Will pˆ from a random sample from a population with 60% successes tend to be closer to 0.6 for a sample size of n = 400 or a sample size of n = 800? Provide an explanation for your choice.
> Two statistics are being considered for estimating the value of a population characteristic. The sampling distributions of the two statistics are shown here. a. Suppose the actual value of the population characteristic is 50. Is Statistic I or Statistic
> Two statistics are being considered for estimating the value of a population characteristic. The sampling distributions of the two statistics are shown here. Explain why Statistic II would be preferred over Statistic I. - Statistic II Statistic I Val
> A 2016 study of 120 U.S. brand-name products found that 70% were active on Snapchat (June 15, 2016, www.businessinsider.com/what-exactly-are-brands-posting-on-snapchat-2016-6, retrieved May 4, 2017). The researchers conducting the study used bootstrap me
> The report titled “One in Three American Households Are Stuck in a Relationship with a Financial Services Provider They Don’t Trust” (June 29, 2016, www.businesswire.com/news /home/20160629005198/en/American-Households-Stuck -Relationship-Financial-Servi
> In mid-2016 the United Kingdom (UK) withdrew from the European Union (an event known as “Brexit”), causing economic concerns throughout the world. One indicator that economists use to monitor the health of the economy
> A survey of a representative sample of 478 U.S. employers found that 359 ranked stress as their top health and productivity concern (June 29, 2016, www.globenewswire.com/news-release/2016/06/29/852338/0/en/Seventy-five-percent-of-U-S-employers-say-stress
> During the 2016 NBA Finals, Kevin Love of the Cleveland Cavaliers successfully made 5 three-point shots out of 19 attempts. Assume that these attempts comprise a sample that is representative of his ability during the entire 2016 season. a. Explain why
> Refer to the instructions given prior to this exercise. The paper “college Students’ Social networking experiences on facebook” (Journal of Applied Developmental Psychology [2009]: 227â€
> Explain why you would not reject the null hypothesis if the P-value were 0.370.
> Explain why a P-value of 0.002 would be interpreted as strong evidence against the null hypothesis.
> For which of the following combinations of P-value and significance level would the null hypothesis be rejected? a. P-value = 0.426 = 0.05 b. P-value = 0.033 = 0.01 c. P-value = 0.046 = 0.10 d. P-value = 0.026 = 0.05 e. P-value = 0.004 = 0
> Step 5 of the five-step process for hypothesis testing is communication of results. What is involved in completing this step?
> The article “euthanasia Still acceptable to Solid majority in U.S.” (www.gallup.com, June 24, 2016, retrieved November 29, 2016) summarized data from a survey of 1025 adult Americans. When asked if doctors should be able to end a terminally ill patient’s
> For which of the following P-values will the null hypothesis be rejected when performing a test with a significance level of 0.05? a. 0.001 b. 0.021 c. 0.078 d. 0.047 e. 0.148
> Step 2 of the five-step process for hypothesis testing is selecting an appropriate method. What is involved in completing this step?
