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 would be needed for 95 percent confidence and an error of ±.20 inch? (Data are from a project by statistics students Lori Bossardet, Shannon Wegner, and Stephanie Rader.)
> Systron Donner Inertial manufactures inertial subsystems for automotive, commercial/ industrial, and aerospace and defense applications. The sensors use a one-piece, micromachined inertial sensing element to measure angular rotational velocity or linear
> The HP dvd1040i 20X Multiformat DVD Writer has an MTBF of 70,000 hours. (a) Assuming continuous operation, what is the probability that the DVD writer will last more than 100,000 hours? (b) Less than 50,000 hours? (c) At least 50,000 hours but not more t
> Suppose the average time to service a Noodles & Company customer at a certain restaurant is 3 minutes and the service time follows an exponential distribution. (a) What is the probability that a customer will be serviced in less than 3 minutes? (b) Why i
> (a) Use Excel functions to calculate the mean and standard deviation for weekend occupancy rates (percent) in nine resort hotels during the off-season. (b) What conclusion would a casual observer draw about center and variability, based on your statistic
> Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P(1.22 < Z < 2.15) b. P(-.00 < Z < 3.00) c. P(-2.00 < Z < 2.00) d. P(Z > 0.50)
> M&Ms are blended in a ratio of 13 percent brown, 14 percent yellow, 13 percent red, 24 percent blue, 20 percent orange, and 16 percent green. Suppose you choose a sample of two M&Ms at random from a large bag. (a) Show the sample space. (b) What is the p
> The U.S. Postal Service will ship a Priority Mail® Large Flat Rate Box (120 3 120 3 51⁄20) anywhere in the United States for a fixed price, regardless of weight. The weights (ounces) of 20 randomly chosen boxes are shown belo
> The durations (minutes) of 26 electric power outages in the community of Sonando Heights over the past five years are shown below. (a) Find the mean, median, and mode. (b) Are the mean and median about the same? (c) Is the mode a good measure of center f
> How many days in advance do travelers purchase their airline tickets? Below are data showing the advance days for a sample of 28 passengers on United Airlines Flight 815 from Chicago to Los Angeles. (a) Calculate the mean, median, mode, and midrange. (b)
> Below are monthly rents paid by 30 students who live off campus. (a) Find the mean, median, and mode. (b) Do the measures of central tendency agree? Explain. (c) Calculate the standard deviation. (d) Sort and standardize the data. (e) Are there outliers
> Chlorine is added to city water to kill bacteria. In a certain year, chlorine content in water from the Lake Huron Water Treatment plant ranged from 0.79 ppm (parts per million) to 0.92 ppm. (a) Use the midrange as a measure of center. (b) Use the Empiri
> Caffeine content in a 5-ounce cup of brewed coffee ranges from 60 to 180 mg, depending on brew time, coffee bean type, and grind. (a) Use the midrange as a measure of center. (b) Use the Empirical Rule to estimate the standard deviation. (c) Why is the a
> Analysis of annualized returns over a 10-year period showed that prepaid tuition plans had a mean return of 6.3 percent with a standard deviation of 2.7 percent, while the Standard & Poor’s 500 stock index had a mean return of 12.9 percent with a standar
> Analysis of portfolio returns over a 20-year period showed the statistics below. (a) Calculate and compare the coefficients of variation. (b) Why would we use a coefficient of variation? Why not just compare the standard deviations? (c) What do the data
> The table below shows average daily sales of Rice Krispies in the month of June in 74 Noodles & Company restaurants. (a) Make a histogram for the data. (b) Would you say the distribution is skewed? (c) Calculate the mean and standard deviation. (d) A
> Find the standard normal area for each of the following, showing your reasoning clearly and indicating which table you used. a. P(0 < Z < 0.50) b. P(-0.50 < Z < 0) c. P(Z > 0) d. P(Z = 0)
> The “expense ratio” is a measure of the cost of managing the portfolio. Investors prefer a low expense ratio, all else equal. Below are expense ratios for 23 randomly chosen stock funds and 21 randomly chosen bond fund
> This year, Dolon Company’s website averaged 12,104 daily views with a standard deviation of 3,026. Last year, the mean number of daily page views was 6,804 with a standard deviation of 1,701. Describe the relative variation in page views in these two yea
> A sample of size n = 70 showed a skewness coefficient of 0.773 and a kurtosis coefficient of 1.277. What is the distribution’s shape?
> A plumbing supplier’s mean monthly demand for vinyl washers is 24,212 with a standard deviation of 6,053. The mean monthly demand for steam boilers is 6.8 with a standard deviation of 1.7. Which demand pattern has more relative variation? Explain.
> At Chipotle Mexican Grill, the number of calories in an order of chips and salsa is normally distributed with a mean of 620 and a standard deviation of 12. Bob’s order had only 580 calories. Was this an outlier? Explain.
> Applicants for a night caretaker position are uniformly distributed in age between 25 and 65. (a) What is the mean age of an applicant? (b) The standard deviation? (c) What is the probability that an applicant will be over 45? (d) Over 55? (e) Between 30
> In a certain year, on average 10 percent of the vehicles tested for emissions failed the test. Suppose that five vehicles are tested. (a) What is the probability that all pass? (b) All but one pass? (c) Sketch the probability distribution and discuss its
> Which of the following could be probability density functions for a continuous random variable? Explain. a. f (x) = .50 for 0 < x < 2 b. f (x) = 2 - x for 0 < x < 2 c. f (x) = .5x for 0 < x < 2
> Which of the following is a continuous random variable? a. Number of Honda Civics sold in a given day at a car dealership. b. Amount of gasoline used for a 200-mile trip in a Honda Civic. c. Distance driven on a particular Thursday by the owner of a Hon
> A sample of 20 pages was taken without replacement from a Yellow Pages directory that has 1,591 pages. (a) Calculate the FPCF for this sample. (b) Should the population be considered effectively infinite?
> 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?
> As a birthday gift, you are mailing a new personal digital assistant (PDA) to your cousin in Toledo. The PDA cost $250. There is a 2 percent chance it will be lost or damaged in the mail. Is it worth $4 to insure the mailing? Explain, using the concept o
> The probability that a 30-year-old white male will live another year is .99863. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?
> A random sample of 30 lunch orders at Noodles and Company showed a mean bill of $10.36 with a standard deviation of $5.31. Find the 95 percent confidence interval for the mean bill of all lunch orders.
> 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. Construct a 95 percent confidence interval for the population standard deviation. (Data are from a project by statistics stud
> To determine the proportion of taxpayers who prefer filing tax returns electronically, a survey of 600 taxpayers was conducted. Calculate the margin of error used to estimate this proportion. What assumptions are required to find the margin of error?
> (a) A poll of 2,277 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have? (b) The poll showed that 44 percent approved the president’s performance. Construct a 90 percent c
> Of 250 college students taking a statistics class, 4 reported an allergy to peanuts. (a) Is the criterion for normality of p met? (b) Assuming that this was a random sample, use MINITAB to construct a 95 per cent confidence interval for the proportion of
> A physician’s billing office conducted a random check of patient records and found that 36 of 50 patients had changed insurance plans within the past year. Construct a 90 percent confidence interval for the true proportion.
> A sample of 213 newspaper tire ads from several Sunday papers showed that 98 contained a low-price guarantee (offer to “meet or beat any price”). (a) Assuming that this was a random sample, construct a 95 percent confidence interval for the proportion of
> Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percen
> July sales for Melodic Kortholt, Ltd., average μ1 = $9,500 with σ1 2 = $1,250. August sales average μ2 = $7,400 with σ2 2 = $1,425. September sales average μ3 = $8,600 with σ3 2 = $1,610. (a) Find the mean and standard deviation of total sales for the th
> A “teen ethics poll” was commissioned by Junior Achievement and Deloitte. The survey by Harris Interactive surveyed 787 students aged 13–18. (a) Assuming that this was a random sample of all students in this age group, find the margin of error of the pol
> A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion
> A poll of 125 college students who watch The Big Bang Theory showed that 83 of them usually watch on a mobile device (e.g., laptop). (a) Assuming that this was a random sample, construct a 90 percent confidence interval for the proportion of all college
> A random sample of 30 cans of Del Vino crushed tomatoes revealed a mean weight of 798.3 grams (excluding the juice). The can-filling process for Del Vino crushed tomatoes has a known standard deviation of 3.1 grams. Construct the 95 percent confidence in
> Junior Achievement and Deloitte commissioned a “teen ethics poll” of 787 students aged 13–18, finding that 29 percent felt inadequately prepared to make ethical judgments. (a) Assuming that this was a random sample, find the 95 percent confidence interva
> How “decaffeinated” is decaffeinated coffee? If a researcher wants to estimate the mean caffeine content of a cup of Starbucks’ decaffeinated espresso with 98 percent confidence and an error of ±0.1 mg, what is the required number of cups that must be te
> A study showed that fourteen of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements for financial records and fraud protection. Assuming that these are a random sample of all publicly traded compa
> The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean. For each substan
> During the Rose Bowl, the length (in seconds) of 12 randomly chosen commercial breaks during timeouts (following touchdown, turnover, field goal, or punt) were Assuming a normal population, construct a 90 percent confidence interval for the mean length
> A random sample of 10 exam scores showed a standard deviation of 7.2 points. Find the 95 percent confidence interval for the population standard deviation. Use Appendix E to obtain the values of X2L and X2U.
> 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
> 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?
> 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?
