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Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions
The Johnson family uses a propane gas grill for cooking outdoors. During the summer they need to replace their tank on average every 30 days. At a randomly chosen moment, what is the probability that they can grill out (a) At least 40 days before they need to replace their tank; (b) No more than 20
At a certain Noodles & Company restaurant, customers arrive during the lunch hour at a rate of 2.8 per minute. What is the probability that (a) At least 30 seconds will pass before the next customer walks in; (b) No more than 15 seconds; (c) More than 1 minute?
The time it takes a ski patroller to respond to an accident call has an exponential distribution with an average equal to 5 minutes.(a) In what time will 90 percent of all ski accident calls be responded to?(b) If the ski patrol would like to be able to respond to 90 percent of the accident calls
Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour.(a) Find the median waiting time until the next telephone order.(b) Find the upper quartile of waiting time before the next telephone order.(c) What is the upper 10 percent of waiting time
Find each uniform continuous probability and sketch a graph showing it as a shaded area.a. P (X < 10) for U (0, 50)b. P (X > 500) for U (0, 1000)c. P (25 < X < 45) for U (15, 65)
A passenger metal detector at Chicago's Midway Airport gives an alarm 0.5 time a minute.(a) Find the median waiting time until the next alarm.(b) Find the first quartile of waiting time before the next alarm.(c) Find the 30th percentile waiting time until the next alarm. Show all calculations
Between 2 a.m. and 4 a.m. at an all-night pizza parlor, the mean time between arrival of telephone pizza orders is 20 minutes. (a) Find the median wait for pizza order arrivals. (b) Explain why the median is not equal to the mean. (c) Find the upper quartile.
The mean life of a certain computer hard disk in continual use is 8 years. (a) How long a warranty should be offered if the vendor wants to ensure that not more than 10 percent of the hard disks will fail within the warranty period? (b) Not more than 20 percent?
Suppose that the distribution of order sizes (in dollars) at L.L. Bean has a distribution that is T(0, 25, 75).(a) Find the mean.(b) Find the standard deviation.(c) Find the probability that an order will be less than $25.(d) Sketch the distribution and shade the area for the event in part (c).
Suppose that the distribution of oil prices ($/bbl) is forecast to be T(50, 65, 105).(a) Find the mean.(b) Find the standard deviation.(c) Find the probability that the price will be greater than $75.(d) Sketch the distribution and shade the area for the event in part (c).
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 Honda Civic.
Which of the following could be probability density functions for a continuous random variable? Explain.a. f (x) = .50 for 0 ≤ x ≤ 2b. f (x) = 2 – x for 0 ≤ x ≤ 2c. f (x) = .5x for 0 ≤ x ≤ 2
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 and 60?
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. Re- search shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.(a) What
Discuss why you would or would not expect each of the following variables to be normally distributed. a. Time for households to complete the U.S. Census short form. b. Size of automobile collision damage claims. c. Diameters of randomly chosen circulated quarters. d. Weight of contents of 16-ounce
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 score was 63.
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 con- centration?(b) The standard deviation?(c) What is the probability that the chlorine concentration will exceed 0.80 ppm on a
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 80 percent d. 5th percentile
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 80 percent
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 percentile?
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 within 2 standard deviations?
The caffeine content of a cup of home-brewed coffee is a normally distributed random vari- able 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 mg of caffeine? (b) Less than 100 mg? (c) A
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 than 590 MPa?(c) Less than 600 MPa?
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 random. (a) What is the probability that the
Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds.(a) What is the mean weight of a randomly chosen vehicle?(b) The standard deviation?(c) What is the probability that a vehicle will weigh less than
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 if the popcorn is cooked for(a) 2
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 proportion of Procyon's production will fail to
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. At a given moment, the water temperature is
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, nd the probability that Bob can finish his job without recharging.
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 allotted time?*(b) If three male customers are
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the prob- ability that the box will contain less than the advertised weight of 453 g?
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 failures in a generating station, the utility can
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 pres- sure.(a) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 135
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.
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.g., X is in pounds and Y is in kilograms),
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 should he choose if he must be at the
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 will not be under filled?(b) A 99 percent
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 percent of the trout they catch?
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 preferred if the procedure must be completed
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?
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?
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?
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 particu- lar neighborhood, what are the first and third quartiles for the number of car accidents in this neighborhood?
A multiple-choice exam has 100 questions. Each question has four choices.(a) What mini- mum 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.
Find the standard error of the mean for each sampling situation (assuming a normal population). What happens to the standard error each time you quadruple the sample size?a. σ = 32, n = 4b. σ = 32, n = 16c. σ = 32, n = 64
Calculate a confidence interval for assuming that each sample is from a normal population. a. x-bar = 24, σ = 3, n = 10, 90 percent confidenceb. x-bar = 125, σ = 8, n = 25, 99 percent confidencec. x-bar = 12.5, σ = 1.2, n = 50, 95 percent confidence
Use the sample information x-bar = 2.4, σ = 0.15, n = 9 to calculate the following confidence intervals for assuming the sample is from a normal population:(a) 90 percent confidence;(b) 95 percent confidence;(c) 99 percent confidence.(d) Describe how the intervals change as you increase the
Use the sample information x-bar = 37, σ = 5, n = 15 to calculate the following confidence intervals for assuming the sample is from a normal population:(a) 90 percent confidence; (b) 95 percent confidence;(c) 99 percent confidence.(d) Describe how the intervals change as you increase the
A random sample of 25 items is drawn from a population whose standard deviation is known to be σ = 40. The sample mean is x-bar = 270.a. Construct an interval estimate for with 95 percent confidence.b. Repeat part a assuming that n 5 50.c. Repeat part a assuming that n 5 100.d. Describe how the
A random sample of 100 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is x-bar = 850.a. Construct an interval estimate for with 95 percent confidence.b. Repeat part a assuming that σ = 100.c. Repeat part a assuming that σ = 200.d. Describe how
The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is normally distributed with a known standard deviation of 1.25 MPG. If a random sample of 10 tanks of gas yields a mean of 21.0 MPG, find the 95 percent confidence interval for the true mean MPG.
Guest ages at a Vail Resorts ski mountain typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5 years.(a) Even though the population distribution of age is - right-skewed, what will be the shape of the distribution of X, the average age, in a random sample of
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000959 mm. If a random sample of 58 sheets of metal resulted in an x-bar = 0.2731 mm, calculate the 99 percent confidence
Find a confidence interval for assuming that each sample is from a normal population.a. x-bar = 24, s = 3, n = 7, 90 percent confidenceb. x-bar = 42, s = 6, n = 18, 99 percent confidencec. x-bar = 119, s = 14, n = 28, 95 percent confidence
For each value of d.f. (degrees of freedom), look up the value of Student's t in Appendix D for the stated level of confidence. Then use Excel to find the value of Student's t to four decimal places. Which method (Appendix D or Excel) do you prefer, and why? a. d.f. = 9, 95 percent confidence b.
Find the standard error of the mean for each sampling situation (assuming a normal population). What happens to the standard error each time you quadruple the sample size?a. σ = 24, n = 9b. σ = 24, n = 36c. σ = 24, n = 144
For each value of d.f. look up the value of Student's t in Appendix D for the stated level of confidence. How close is the t-value to the corresponding z-value (at the bottom of the column for d.f. = ∞) ? a. d.f. = 40, 95 percent confidence b. d.f. = 80, 95 percent confidence c. d.f. = 100, 95
A random sample of 10 items is drawn from a population whose standard deviation is unknown. The sample mean is x-bar = 270 and the sample standard deviation is s = 20. Use Appendix D to find the values of Student's t.a. Construct an interval estimate for with 95 percent confidence.b. Repeat part a
A random sample of 25 items is drawn from a population whose standard deviation is unknown. The sample mean is x-bar = 850 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student's t.a. Construct an interval estimate of with 95 percent confidence.b. Repeat part a
A sample of 21 minivan electrical warranty repairs for "loose, not attached" wires (one of several electrical failure categories the dealership mechanic can select) showed a mean repair cost of $45.66 with a standard deviation of $27.79.(a) Construct a 95 percent confidence interval for the true
A random sample of 16 pharmacy customers showed the waiting times below (in minutes). Find a 90 percent confidence interval for, assuming that the sample is from a normal population.
A random sample of monthly rent paid by 12 college seniors living off campus gave the results below (in dollars). Find a 99 percent confidence interval for , assuming that the sample is from a normal population.
A random sample of 10 shipments of stick-on labels showed the following order sizes.(a) Construct a 95 percent confidence interval for the true mean order size.(b) How could the confidence interval be made narrower? (Data are from a project by MBA student Henry Olthof Jr.)
Prof. Green gave three exams last semester. Scores were normally distributed on each exam. Below are scores for 10 randomly chosen students on each exam.(a) Find the 95 percent confidence interval for the mean score on each exam.(b) Do the confidence intervals overlap? What inference might you draw
Calculate the standard error of the sample proportion.a. n = 30, π = .50b. n = 50, π = .20c. n = 100, π = .10d. n = 500, π = .005
Should p be assumed normal? a. n = 25, π = .50 b. n = 60, π = 20 c. n = 100, π = .08
Find the interval [μ– z σ / √ n μ + z σ / √ n] within which 90 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.a. μ = 100, σ = 12, n = 36b. μ = 2,000 σ = 150, n = 9c. μ = 500, σ = 10, n = 25
Find the margin of error for a poll, assuming that π = 50.a. n = 50b. n = 200c. n = 500d. n = 2,000
A car dealer is taking a customer satisfaction survey. Find the margin of error (i.e, assuming 95% confidence and π = .50) for(a) 250 respondents,(b) 125 respondents, and(c) 65 respondents.
In a sample of 500 new websites registered on the Internet, 24 were anonymous (i.e., they shielded their name and contact information).(a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous.(b) May normality of p be assumed? Explain.
From a list of stock mutual funds, 52 funds were selected at random. Of the funds chosen, it was found that 19 required a minimum initial investment under $1,000.(a) Construct a 90 percent confidence interval for the true proportion requiring an initial investment under $1,000.(b) May normality of
Of 43 bank customers depositing a check, 18 received some cash back.(a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back.(b) Check the normality assumption of p.
A survey showed that 4.8 percent of the 250 Americans surveyed had suffered some kind of identity theft in the past 12 months.(a) Construct a 99 percent confidence interval for the true proportion of Americans who had suffered identity theft in the past 12 months.(b) May normality of p be assumed?
A sample of 50 homes in a subdivision revealed that 24 were ranch style (as opposed to colonial, tri-level, or Cape Cod). (a) Construct a 95 percent confidence interval for the true proportion of ranch style homes. (b) Check the normality assumption of p. 8.37 In a grocery parking lot, 32 of 136
In a grocery parking lot, 32 of 136 cars selected at random were white.(a) Construct a 99 percent confidence interval for the true proportion of white cars.(b) May normality of p be assumed? Explain.
Calculate the FPCF for each sample and population size. Can the population be considered effectively in finite in each case?a. N = 450, n = 10b. N = 300, n = 25c. N = 1800, n = 280
Use the following information x-bar = 50, σ = 15, n = 90, N = 1,000--to calculate confidence intervals for assuming the sample is from a normal population:(a) 90 percent confidence;(b) 95 percent confidence;(c) 99 percent confidence.
Find ht interval [ μ – z σ / √ n μ + z σ / √ n = within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.a. μ = 200, σ = 12, n = 36b. μ = 1,000, σ = 15, n = 9c. μ = 50, σ = 1, n = 25
Use the following information x-bar = 3.7, s = 0.2, n = 1,200, N = 5,800--to calculate confidence intervals for assuming the sample is from a normal population:(a) 90 percent confidence;(b) 95 percent confidence;(c) 99 percent confidence.
A random survey of 500 students was conducted from a population of 2,300 students to estimate the proportion who had part-time jobs. The sample showed that 245 had part-time jobs. Calculate the 90 percent confidence interval for the true proportion of students who had part-time jobs.
For each level of precision, find the required sample size to estimate the mean starting salary for a new CPA with 95 percent confidence, assuming a population standard deviation of $7,500 (same as last year).a. E = $2,000b. E = $1,000c. E = $500
Last year, a study showed that the average ATM cash withdrawal took 65 seconds with a standard deviation of 10 seconds. The study is to be repeated this year. How large a sample would be needed to estimate this year's mean with 95 percent confidence and an error of ±4 seconds?
The EPA city/hwy mpg range for a Saturn Vue FWD automatic 5-speed transmission is 20 to 28 mpg.(a) Estimate using Method 3 from Table 8.11.(b) If you owned this vehicle, how large a sample (e.g., how many tanks of gas) would be required to estimate your mean mpg with an error of ±1 mpg and 90
Popcorn kernels are believed to take between 100 and 200 seconds to pop in a certain micro- wave.(a) Estimate using Method 3 from Table 8.11.(b) What sample size (number of kernels) would be needed to estimate the true mean seconds to pop with an error of 65 seconds and ±5 percent confidence?
Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year's mean arrival rate with 98 percent confidence and an error of ±0.5?
In an intra-squad swim competition, men's freestyle 100 swim times at a certain university ranged from 43.89 seconds to 51.96 seconds.(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution).(b) What sample size is needed to estimate the mean for all
The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5-speed using regular gas is a normally distributed random variable with a range 16 MPG to 21 MPG.(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution).(b) What sample size is
The diameter of bushings turned out by a manufacturing process is a normally distributed random variable with a mean of 4.035 mm and a standard deviation of 0.005 mm. A sample of 25 bushings is taken once an hour.(a) Within what interval should 95 percent of the bushing diameters fall?(b) Within
What sample size would be required to estimate the true proportion of American female business executives who prefer the title "Ms.," with an error of ±0.025 and 98 percent confidence?
What sample size would be needed to estimate the true proportion of American households that own more than one DVD player, with 90 percent confidence and an error of ±0.02?
What sample size would be needed to estimate the true proportion of students at your college (if you are a student) who are wearing backpacks, with 95 percent confidence and an error of ±0.04?
What sample size would be needed to estimate the true proportion of American adults who know their cholesterol level, using 95 percent confidence and an error of ±0.02?
How large a sample size would be needed to estimate the percentage of wireless routers in San Francisco that use data encryption, with an error of ±2 percent and 95 percent confidence?
Inspection of a random sample of 19 aircraft showed that 15 needed repairs to x a wiring problem that might compromise safety. How large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidence and an error of ±6 percent?
Find the 95 percent confidence interval for the population variance from these samples. a. n = 15 commuters, s = 10 miles driven b. n = 18 students, s = 12 study hours
The weights of 20 oranges (in ounces) are shown below. Construct a 95 percent confidence interval for the population standard deviation.
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. Construct a 95 percent confidence interval for the population variance. (Data are from a project by statistics students Lori Bossardet,
Find the 90 percent confidence interval for the standard deviation of gasoline mileage mpg for these 16 San Francisco commuters driving hybrid gas-electric vehicles.
The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 25.0 MPG - and a standard deviation of σ = 1.25 MPG.(a) What is the standard error of X-bar, the mean from a random sample of 16 fill-ups
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.
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