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 can?
> 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?
> 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 numbe
> 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
> 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)
> Find the data value that corresponds to each of the following z-scores. a. Final exam scores: Allison’s z-score = 2.30, μ = 74, σ = 7 b. Weekly grocery bill: James’ z-score = 21.45, μ = $53, σ = $12 c. Daily video game play time: Eric’s z-score = 20.79,
> SAT scores for the entering class of 2010 at Oxnard University were normally distributed with a mean of 1340 and a standard deviation of 90. Bob’s SAT score was 1430. (a) Find Bob’s standardized z-score. (b) By the Empirical Rule, is Bob’s SAT score unus
> Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2731 mm with a standard deviation of 0.000959 mm. (a) A certain shipment has
> Bags of jelly beans have a mean weight of 396 gm with a standard deviation of 5 gm. Use Chebyshev’s Theorem to find a lower bound for the number of bags in a sample of 200 that weigh between 386 and 406 gm.
> During a rock concert, the noise level (in decibels) in front row seats has a mean of 95 dB with a standard deviation of 8 dB. Without assuming a normal distribution, find the minimum percentage of noise level readings within 3 standard deviations of the
> For each data set: (a) Find the mean, median, and mode. (b) Which, if any, of these three measures is the weakest indicator of a “typical” data value? Why? a. 100 m dash times (n = 6 top runners): 9.87, 9.98, 10.0
> If the mean asset turnover for retail firms is 2.02 with a standard deviation of 0.22, without assuming a normal distribution, within what range will at least 75% of retail firms’ asset turnover fall?
> (a) For each data set, calculate the mean, median, and mode. (b) Which, if any, of these three measures is the weakest indicator of a “typical” data value? Why? a. Number of e-mail accounts (12 students): 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3 b. Number of
> Prior to starting a recycling program, a city decides to measure the quantity of garbage produced by single-family homes in various neighborhoods. This experiment will require weighing garbage on the day it is set out. (a) What sampling method would you
> The National Claims History (NCH) contains records for 999,645 Medicare patients who were discharged from acute care hospitals in October 2008. The Department of Health and Human Services performed a detailed audit of adverse medical events on a random s
> 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) Calcula
> Examine each of the following statistics. Which sampling method was most likely to have been used (simple random, systematic, stratified, cluster)? a. A survey showed that 30 percent of U.S. businesses have fi red an employee for inappropriate web surfi
> A financial magazine publishes an annual list of major stock funds. Last year, the list contained 1,699 funds. What method would you recommend to obtain a sample of 20 stock funds to estimate the 10-year percent return?
> Would you expect Noodles & Company to use a sample or census to measure each of the following? Explain. a. The annual average weekly revenue of each Noodles restaurant. b. The average number of weekly lunch visits by customers. c. The customer satisfact
> Would you expect Starbucks to use a sample or census to measure each of the following? Explain. a. The percentage of repeat customers at a certain Starbucks on Saturday mornings. b. The number of chai tea latte orders last Saturday at a certain Starbuck
> Arsenic (a naturally occurring, poisonous metal) in home water wells is a common threat. (a) What sampling method would you use to estimate the arsenic levels in wells in a rural county to see whether the samples violate the EPA limit of 10 parts per bil
> The General Accounting Office conducted random testing of retail gasoline pumps in Michigan, Missouri, Oregon, and Tennessee. The study concluded that 49 percent of gasoline pumps nationwide are mislabeled by more than one-half of an octane point. What k
> The IRS estimates that the average taxpayer spent 3.7 hours preparing Form 1040 to fi le a tax return. Could a census be used to update this estimate for the most recent tax year? Why or why not?
> There are 327 official ports of entry in the United States. The Department of Homeland Security selects 15 ports of entry at random to be audited for compliance with screening procedures of incoming travelers through the primary and secondary vehicle and
> A certain health maintenance organization (HMO) is studying its daily office routine. They collect information on three variables: the number of patients who visit during a day, the patient’s complaint, and the waiting time until each patient sees a doct
> Recently, researchers estimated that 76.8 percent of global e-mail traffic was spam. Could a census be used to update this estimate? Why or why not?
> 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
> Is each of the following a parameter or statistic? a. The number of visits to a pediatrician’s office last week. b. The number of copies of John Grisham’s most recent novel sold to date. c. The total revenue realized from sales of John Grisham’s most re
> Is each of the following a parameter or a statistic? If you are uncertain, explain the issues. a. The number of cans of Campbell’s soup sold last week at your local supermarket. b. The proportion of all soup in the United States that was sold under the
> Would you use a sample or census to measure each of the following? a. The number of workers currently employed by Campbell Soup Company. b. The average price of a can of Campbell’s Cream of Mushroom soup. c. The total earnings of workers employed by Cam
> Would you use a sample or a census to measure each of the following? Why? If you are uncertain, explain the issues. a. The number of cans of Campbell’s soup on your local supermarket’s shelf today at 6:00 p.m. b. The proportion of soup sales last week i
> Identify the following data as either time series or cross-sectional. a. The number of rooms booked each night for the month of January 2014 at a Vail Resorts hotel. b. The amount spent on books at the start of this semester by each student in your stat
> Identify the following data as either time series or cross-sectional. a. The 2014 CEO compensation of the 500 largest U.S. companies. b. The annual compensation for the CEO of Coca-Cola Enterprises from 2000 to 2014. c. The weekly revenue for a Noodles
> Below are five questions from a survey of MBA students. Answers were written in the blank at the left of each question. For each question, state the data type (categorical, discrete numerical, or continuous numerical) and measurement level (nominal, ordi
> Below are five questions from a survey of MBA students. Answers were written in the blank at the left of each question. For each question, state the data type (categorical, discrete numerical, or continuous numerical) and measurement level (nominal, ordi
> Below are five questions from a survey of MBA students. Answers were written in the blank at the left of each question. For each question, state the data type (categorical, discrete numerical, or continuous numerical) and measurement level (nominal, ordi
> Which measurement level (nominal, ordinal, interval, ratio) is each of the following variables? a. Number of annual office visits by a particular Medicare subscriber. b. Daily caffeine consumption by a six-year-old child. c. Type of vehicle driven by a
> According to J.D. Power and Associates’ 2006 Initial Quality Study, consumers reported on average 1.7 problems per vehicle with new 2006 Volkswagens. In a randomly selected new Volkswagen, find the probability of (a) at least one problem; (b) no problems
> Which measurement level (nominal, ordinal, interval, ratio) is each of the following variables? a. A customer’s ranking of five new hybrid vehicles. b. Noise level 100 meters from the Dan Ryan Expressway at a randomly chosen moment. c. Number of occupan
> Which type of data (categorical, discrete numerical, continuous numerical) is each of the following variables? a. Number of spectators at a randomly chosen Wimbledon tennis match. b. Water consumption (liters) by a randomly chosen Wimbledon player durin
> Which type of data (categorical, discrete numerical, continuous numerical) is each of the following variables? a. Age of a randomly chosen tennis player in the Wimbledon tennis tournament. b. Nationality of a randomly chosen tennis player in the Wimbled
> The first Rose Bowl (football) was played in 1902. The next was not played until 1916, but a Rose Bowl has been played every year since then. The margin of victory in each of the 95 Rose Bowls from 1902 through 2011 is shown below (0 indicates a tie). (a
> A study of 40 U.S. cardiac care centers showed the following ratios of nurses to beds. (a) Prepare a dot plot. (b) Prepare a frequency distribution and histogram (you may either specify the bins yourself or use automatic bins). (c) Describe the distribut
> A research study showed that adolescents who watched more than 4 hours of TV per day were more than five times as likely to start smoking as those who watched less than 2 hours a day. The researchers speculate that TV actors’ portrayals of smoking as per
> (a) Use Excel to prepare a line chart to display the skier/snowboarder data. Modify the default colors, fonts, etc., to make the display effective. (b) Describe the pattern, if any. U.S. Skier/Snowboarder Visits (Millions), 1984–2007 Season Visits S
> A European study of thousands of men found that the PSA screening for prostate cancer reduced the risk of a man’s dying from prostate cancer from 3.0 percent to 2.4 percent. “But it’s already a small risk. I don’t think a difference of less than 1 percen
> “Lacrosse helmets are not needed,” said Tom. “None of the guys on my team have ever had head injuries.” Is there a fallacy in Tom’s reasoning? Explain.
