The probability of being in a car accident when driving more than 10 miles over the speed limit in a residential neighborhood is .06. Of the next 1,000 cars that pass through a particular neighborhood, what are the first and third quartiles for the number of car accidents in this neighborhood?
> Four hundred automobiles are to be inspected for California emissions compliance. Of these, 320 actually are compliant but 80 are not. A random sample of 6 cars is chosen. (a) Justify the use of the binomial approximation. (b) What is the probability tha
> A pediatrician’s records showed the mean height of a random sample of 25 girls at age 12 months to be 29.530 inches with a standard deviation of 1.0953 inches. (a) Construct a 95 percent confidence interval for the true mean height. (b) What sample size
> Twenty-one warranty repairs were selected from a population of 126 by selecting every sixth item. The population consisted of “loose, not attached” minivan electrical wires (one of several electrical failure categories the dealership mechanic can select)
> Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636
> Sixteen owners of 2010 Audi A4 sedans kept track of their average fuel economy for a month. The results are shown below. (a) Construct a 95 percent confidence interval for the mean. (b) What factor(s) limit the conclusions that can be drawn about the tru
> Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. (a) Calculate the FPCF for this sample. (b) Should the population be considered effectively infin
> Statistics students were asked to go home and fill a 1-cup measure with raisin bran, tap the cup lightly on the counter three times to settle the contents, if necessary add more raisin bran to bring the contents exactly up to the 1-cup line, spread the c
> Vail Resorts would like to send a survey to their guests asking about their satisfaction with the new 2009 website design. They would like to have a margin of error of ±5 percent on responses with 95 percent confidence. (A) Using the conservative approac
> If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?
> The time it takes to give a man a shampoo and haircut is normally distributed with mean 22 minutes and standard deviation 3 minutes. Customers are scheduled every 30 minutes. (a) What is the probability that a male customer will take longer than the allo
> Tests show that, on average, the Li-ion Hitachi stick driver can drive 207 drywall screws on a single charge. Bob needs to drive 230 drywall screws. If the standard deviation is 14 screws, find the probability that Bob can finish his job without rechargi
> A law enforcement agency processes 500 background checks for firearms purchasers. Fifty applicants are convicted felons. Through a clerk’s error, 10 applicants are approved without checking for felony convictions. (a) Justify the use of the binomial appr
> Procyon Manufacturing produces tennis balls. Their manufacturing process has a mean ball weight of 2.035 ounces with a standard deviation of 0.03 ounce. Regulation tennis balls are required to have a weight between 1.975 ounces and 2.095 ounces. What pro
> Past insurance company audits have found that 2 percent of dependents claimed on an employee’s health insurance actually are ineligible for health benefits. An auditor examines a random sample of 7 claimed dependents. (a) What is the probability that all
> Demand for residential electricity at 6:00 p.m. on the first Monday in October in Santa Theresa County is normally distributed with a mean of 4,905 MW (megawatts) and a standard deviation of 355 MW. Due to scheduled maintenance and unexpected system fail
> Car security alarms go off at a mean rate of 3.8 per hour in a large Costco parking lot. Find the probability that in an hour there will be (a) no alarms; (b) fewer than four alarms; and (c) more than five alarms.
> The length of a time-out during a televised professional football game is normally distributed with a mean of 84 seconds and a standard deviation of 10 seconds. If the network runs consecutive commercials totaling 90 seconds, what is the probability that
> In a recent year, potentially dangerous commercial aircraft incidents (e.g., near collisions) averaged 1.2 per 100,000 flying hours. Let X be the number of incidents in a 100,000-hour period. (a) Justify the use of the Poisson model. (b) What is the prob
> In the last 50 years, the average number of deaths due to alligators in Florida is 0.3 death per year. Assuming no change in this average, in a given year find the probability of (a) no alligator deaths; (b) at least 2 alligator deaths.
> Shower temperature at the Oxnard Health Club showers is regulated automatically. The heater kicks in when the temperature falls to 998F and shuts off when the temperature reaches 1078F. Water temperature then falls slowly until the heater kicks in again.
> Lunch customers arrive at a Noodles & Company restaurant at an average rate of 2.8 per minute. Define X to be the number of customers to arrive during a randomly selected minute during the lunch hour and assume X has a Poisson distribution. (a) Calculate
> Noodles & Company wants to estimate the percent of customers who order dessert, with 95 percent confidence and an error of ±10%. What is the required sample size?
> Two hundred employee travel expense reimbursement vouchers were filed last year in the finance department at Ramjac Corporation. Of these, 20 contained errors. A corporate auditor audits a sample of five vouchers. Let X be the number of incorrect voucher
> Tire pressure in a certain car is a normally distributed random variable with mean 30 psi (pounds per square inch) and standard deviation 2 psi. The manufacturer’s recommended correct inflation range is 28 psi to 32 psi. A motorist’s tire is inspected at
> The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? (b) More
> The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. (a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 m
> Write the Excel formula for each Poisson probability, using a mean arrival rate of 10 arrivals per hour. a. Seven arrivals. b. Three arrivals. c. Fewer than five arrivals. d. At least 11 arrivals.
> A study by the Parents’ Television Council showed that 80 percent of movie commercials aired on network television between 8 and 9 p.m. (the prime family viewing hour) were for R-rated films. (a) Find the probability that in 16 commercials during this ti
> Experience indicates that 8 percent of the pairs of men’s trousers dropped off for dry cleaning will have an object in the pocket that should be removed before cleaning. Suppose that 14 pairs of pants are dropped off and the cleaner forgets to check the
> A random sample of 30 lunch orders at Noodles and Company showed a standard deviation of $5.31. Find the 90 percent confidence interval for the population standard deviation. Use Excel to obtain X2L =CHISQ.INV(α/2,d.f.) and X2U =CHISQ.INV.RT(α/2,d.f.)
> Scores on a certain accounting exam were normally distributed with a mean of 75 and a standard deviation of 7. Find the percentile for each individual using Excel’s =NORM.S.DIST function. (a) Bob’s score was 82; (b) Phyllis’s score was 93; (c) Tom’s scor
> Write the Excel binomial formula for each probability. a. Three successes in 20 trials with a 30 percent chance of success. b. Seven successes in 50 trials with a 10 percent chance of success. c. Six or fewer successes in 80 trials with a 5 percent chan
> Why might the following not be normally distributed? (a) The time it takes you to drive to the airport. (b) The annual income for a randomly chosen Major League Baseball player. (c) The annual hurricane losses suffered by homeowners in Florida.
> (a) Check whether the binomial approximation is acceptable in each of the following hypergeometric situations. (b) Find the binomial approximation (using Appendix A) for each probability requested. (c) Check the accuracy of your approximation by using Ex
> Discuss why you would or would not expect each of the following variables to be normally distributed. Hint: Would you expect a single central mode and tapering tails? Would the distribution be roughly symmetric? Would one tail be longer than the other?
> In a sample of 100 Planter’s Mixed Nuts, 19 were found to be almonds. (a) Construct a 90 percent confidence interval for the true proportion of almonds. (b) May normality be assumed? Explain. (c) What sample size would be needed for 90 percent confidence
> John can take either of two routes (A or B) to LAX airport. At midday on a typical Wednesday the travel time on either route is normally distributed with parameters μA = 54 minutes, σA = 6 minutes, μB = 60 minutes, and σB = 3 minutes. (a) Which route sho
> Are the following statements true or false? Explain your reasoning. a. “If we see a standardized z-value beyond 63, the variable cannot be normally distributed.” b. “If X and Y are two normally distributed random variables measured in different units (e
> A statistics exam was given. Calculate the percentile for each of the following four students. a. John’s z-score was -1.62. b. Mary’s z-score was 0.50. c. Zak’s z-score was 1.79. d. Frieda’s z-score was 2.48.
> The length of a brook trout is normally distributed. Two brook trout are caught. (a) What is the probability that both exceed the mean? (b) Neither exceeds the mean? (c) One is above the mean and one is below? (d) Both are equal to the mean?
> Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 28 minutes and a standard deviation of 4 minutes, while method B has a mean of 32 minutes and a standard deviation of 2 minutes. (a) Which procedure is
> The length of a certain kind of Colorado brook trout is normally distributed with a mean of 12.5 inches and a standard deviation of 1.2 inches. What minimum size limit should the Department of Natural Resources set if it wishes to allow people to keep 80
> The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 5 ml. The mean is adjustable. (a) Where should the mean be set to ensure a 95 percent probability that a half-liter bottle wil
> A test for ovarian cancer has a 5 percent rate of false positives and a 0 percent rate of false negatives. On average, 1 in every 2,500 American women over age 35 actually has ovarian cancer. If a woman over 35 tests positive, what is the probability tha
> A medical laboratory receives 40 blood specimens to check for HIV. Eight actually contain HIV. A worker is accidentally exposed to five specimens. (a) Use Excel to calculate the entire hypergeometric probability distribution. (b) What is the probability
> Dolon Web Security Consultants requires all job applicants to submit to a test for illegal drugs. If the applicant has used illegal drugs, the test has a 90 percent chance of a positive result. If the applicant has not used illegal drugs, the test has an
> A biometric security device using fingerprints erroneously refuses to admit 1 in 1,000 authorized persons from a facility containing classified information. The device will erroneously admit 1 in 1,000,000 unauthorized persons. Assume that 95 percent of
> In CABG surgery, there is a .00014 probability of a retained foreign body (e.g., a sponge or a surgical instrument) left inside the patient. (a) In 100,000 CABG surgeries, what is the expected number of retained foreign bodies? (b) What is the Poisson ap
> Among live deliveries, the probability of a twin birth is .02. (a) In 2,000 live deliveries, what is the probability of at least 50 twin births? (b) Fewer than 35?
> At a certain fire station, false alarms are received at a mean rate of 0.2 per day. In a year, what is the probability that fewer than 60 false alarms are received?
> On a cold morning the probability is .02 that a given car will not start in the small town of Eureka. Assume that 1,500 cars are started each cold morning. (a) What is the probability that at least 25 cars will not start? (b) More than 40?
> The probability that a certain kind of flower seed will germinate is .80. (a) If 200 seeds are planted, what is the probability that fewer than 150 will germinate? (b) That at least 150 will germinate?
> A multiple-choice exam has 100 questions. Each question has four choices. (a) What minimum score should be required to reduce the chance of passing by random guessing to 5 percent? (b) To 1 percent? (c) Find the quartiles for a guesser.
> Nationwide, the probability that a rental car is from Hertz is 25 percent. In a sample of 100 rental cars, what is the probability that fewer than 20 are from Hertz?
> On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below. (a) Calculate the mean and standard deviation. (b) Describe the shape of this distribution. 1 2 4. Total P(x) .05 .30 .
> On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day. (a) Find P(
> The probability of an incorrect call by an NFL referee is .025 (e.g., calling a pass complete, but the decision reversed on instant replays). In a certain game, there are 150 plays. (a) What is the probability of at least 4 incorrect calls by the referee
> On average, 2 percent of all persons who are given a breathalyzer test by the state police pass the test (blood alcohol under .08 percent). Suppose that 500 breathalyzer tests are given. (a) What is the expected number who pass the test? (b) What is the
> The probability of being “bumped” (voluntarily or involuntarily) on a U.S. airline was .00128. The average number of passengers traveling through Denver International Airport each hour is 5,708. (a) What is the expected number of bumped passengers per ho
> The probability is .03 that a passenger on United Airlines Flight 9841 is a Platinum flyer (50,000 miles per year). If 200 passengers take this flight, use Excel to find the binomial probability of (a) no Platinum flyers, (b) one Platinum flyer, and (c)
> Among live deliveries, the probability of a twin birth is .02. (a) In 200 live deliveries, how many would be expected to have twin births? (b) What is the probability of no twin births? (c) One twin birth? (d) Calculate these probabilities both with and
> How many riders would there have to be on a bus to yield (a) a 50 percent probability that at least two will have the same birthday? (b) A 75 percent probability? Hint: Use the Learning Stats demonstration from McGraw-Hill’s Connect.
> Leaks occur in a pipeline at a mean rate of 1 leak per 1,000 meters. In a 2,500-meter section of pipe, what is the probability of (a) no leaks? (b) Three or more leaks? (c) What is the expected number of leaks?
> On New York’s Verrazano Narrows bridge, traffic accidents occur at a mean rate of 2.0 crashes per day. Let X be the number of crashes in a given day. (a) Justify the use of the Poisson model. (b) What is the probability of at least one crash? (c) Fewer t
> In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.2 quakes per year. Let X be the number of quakes in a given year. (a) Justify the use of the Poisson model. (b) What is the probability of fewer than three quakes? (c) More than five qua
> A “rogue wave” (one far larger than others surrounding a ship) can be a threat to ocean-going vessels (e.g., naval vessels, container ships, oil tankers). The European Centre for Medium Range Weather Forecasts issues a warning when such waves are likely.
> Fifty employee travel expense reimbursement vouchers were filed last quarter in the finance department at Ramjac Corporation. Of these, 20 contained errors. A corporate auditor inspects five vouchers at random. Let X be the number of incorrect vouchers i
> Jim’s systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim’s age group, 140 is the threshold for high blood pressure. (a) If Jim’s systolic blood pressure is taken at a randomly chosen moment,
> In a certain automobile manufacturing paint shop, paint defects on the hood occur at a mean rate of 0.8 defect per square meter. A hood on a certain car has an area of 3 square meters. (a) Justify the use of the Poisson model. (b) If a customer inspects
> A sample of 40 CDs from a student’s collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. (a) Construct a 95 percent confidence interval for the mean. (b) Why might the normality assumption be an issue here? (c) Wha
> At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per day on a typical Wednesday. Let X be the number of cancellations on a particular Wednesday. (a) Justify the use of the Poisson model. (b) What is the probabi
> Dave the jogger runs the same route every day (about 2.2 miles). On 18 consecutive days, he recorded the number of steps using a pedometer. The results were (a) Construct a 95 percent confidence interval for the true mean number of steps Dave takes on
> In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds. What percentage of the kernels will fail to pop
> In a major league baseball game, the average is 1.0 broken bat per game. Find the probability of (a) no broken bats in a game; (b) at least 2 broken bats.
> The weekly demand for Baked Lay’s potato chips at a certain Subway sandwich shop is a random variable with mean 450 and standard deviation 80. Find the value(s) of X for each event. Show your work. a. Highest 50 percent b. Lowest 25 percent c. Middle 8
> Software filters rely heavily on “blacklists” (lists of known “phishing” URLs) to detect fraudulent e-mails. But such filters typically catch only 20 percent of phishing URLs. Jason receives 16 phishing e-mails. (a) What is the expected number that would
> Why might the number of calls received per minute at a fire station not be a Poisson event?
> A statistics textbook chapter contains 60 exercises, 6 of which are essay questions. A student is assigned 10 problems. Define X to be the number of essay questions the student receives. (a) Use Excel to calculate the entire hypergeometric probability di
> Chlorine concentration in a municipal water supply is a uniformly distributed random variable that ranges between 0.74 ppm and 0.98 ppm. (a) What is the mean chlorine concentration? (b) The standard deviation? (c) What is the probability that the chlo
> Although television HDTV converters are tested before they are placed in the installer’s truck, the installer knows that 20 percent of them still won’t work properly. The driver must install eight converters today in an apartment building. (a) Ten conver
> A small feeder airline knows that the probability is .10 that a reservation holder will not show up for its daily 7:15 a.m. flight into a hub airport. The flight carries 10 passengers. (a) If the flight is fully booked, what is the probability that all t
> The length of a Colorado brook trout is normally distributed. (a) What is the probability that a brook trout’s length exceeds the mean? (b) Exceeds the mean by at least 1 standard deviation? (c) Exceeds the mean by at least 2 standard deviations? (d) Is
> The amounts spent by customers at a Noodles & Company restaurant during lunch are normally distributed with a mean equal to $7.00 and a standard deviation equal to $0.35. (a) What amount is the first quartile? (b) The second quartile? (c) The 90th percen
> The weekly demand for Papa Chubby’s pizzas on a Friday night is a random variable with mean 235 and standard deviation 10. Find the value(s) of X for each event. Show your work. a. Lowest 50 percent b. Highest 25 percent c. 90th percentile d. Middle 8
> The default rate on government-guaranteed student loans at a certain private 4-year institution is 7 percent. The college extends 10 such loans. (a) What is the probability that none of them will default? (b) That at least three will default? (c) What is
> Tired of careless spelling and grammar, a company decides to administer a test to all job applicants. The test consists of 20 sentences. Applicants must state whether each sentence contains any grammar or spelling errors. Half the sentences contain error
> Passengers using New York’s MetroCard system must swipe the card at a rate between 10 and 40 inches per second, or else the card must be re-swiped through the card reader. Research shows that actual swipe rates by subway riders are uniformly distributed
> On average, 40 percent of U.S. beer drinkers order light beer. (a) What is the probability that none of the next eight customers who order beer will order light beer? (b) That one customer will? (c) Two customers? (d) Fewer than three? (e) Construct the
> (a) State the values that X can assume in each hypergeometric scenario. (b) Use the hypergeometric PDF formula to find the probability requested. (c) Check your answer by using Excel. i. N = 10, n = 3, s = 4, P(X = 3) ii. N = 20, n = 5, s = 3, P(X = 2)
> In a certain Kentucky Fried Chicken franchise, half of the customers typically request “crispy” instead of “original.” (a) What is the probability that none of the next four customers will request “crispy”? (b) At least two? (c) At most two? (d) Construc
> The probability that an American CEO can transact business in a foreign language is .20. Ten American CEOs are chosen at random. (a) What is the probability that none can transact business in a foreign language? (b) That at least two can? (c) That all 10
> A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
> There is a 14 percent chance that a Noodles & Company customer will order bread with the meal. Use Excel to find the probability that in a sample of 10 customers (a) more than five will order bread; (b) no more than two will; (c) none of the 10 will ord
> Consider the Bernoulli model. What would be a typical probability of success (π) for (a) free throw shooting by a good college basketball player? (b) Hits by a good baseball batter? (c) Passes completed by a good college football quarterback? (d) Incorre
> A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necess
> Use Excel to generate 1,000 random integers in the range 1 through 5. (a) What are the expected mean and standard deviation? (b) Show the Excel formula you used.
> A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter of 0.834343 inch with a standard deviation of 0.001886 inch. (a) Why would nickel diameters vary? (b) Construct a 99 percent confidence interval for the true me
> The number of blueberries in a blueberry muffin baked by Earth Harvest Bakeries can range from 18 to 30 blueberries. (a) Use the Empirical Rule to estimate the standard deviation of the number of blueberries in a muffin. (b) What assumption did you make
> The average time a Boulder High varsity lacrosse player plays in a game is 30 minutes with a standard deviation of 7 minutes. Nolan’s playing time in last week’s game against Fairview was 48 minutes. (a) Calculate the z-score for Nolan’s playing time aga
> Three percent of the letters placed in a certain postal drop box have incorrect postage. Suppose 200 letters are mailed. (a) For this binomial, what is the expected number with incorrect postage? (b) For this binomial, what is the standard deviation? (c)
