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Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions

(a) Find the coefficient of variation for prices of these three stocks.(b) Which stock has the greatest relative variation?(c) To measure variability, why not just compare the standard deviations?
Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.(a) Find the sample mean, standard deviation, and coefficient of variation for each quiz.(b) How do these data sets differ in terms of center and variability?(c) Brie y describe and compare student
Noodles and Company tested consumer reaction to two spaghetti sauces. Each of 70 raters assessed both sauces on a scale of 1 (worst) to 10 (best) using several taste criteria. To correct for possible bias in tasting order, half the raters tasted Sauce A first, while the other half tasted Sauce B
(a) By Chebychev's Theorem, at least how many students in a class of 200 would score within the range μ ± 2σ ?(b) By the Empirical Rule, how many students in a class of 200 would score within the range μ ± 2σ ?
An exam has a mean of 70 with a standard deviation of 10. Use Chebyshev's Theorem to find a lower bound for the number of students in a class of 400 who scored between 50 and 90.
The mean monthly rent of students at Oxnard University is $875 with a standard deviation of $219.(a) John's rent is $1,325. What is his standardized z-score?(b) Is John's rent an outlier?(c) How high would the rent have to be to qualify as an outlier?
Convert each individual X data value to a standardized Z value and interpret it. a. Class exam: John's score is 91, μ = 79, σ = 5 b. Student GPA: Mary's GPA is 3.18, μ = 2.87, σ = 0.31 c. Weekly study hours: Jaime studies 18 hours, μ = 15.0, σ = 5.0
For each data set, which best indicates a "typical" data value (mean, median, either)? a. MPG for 7 Honda Civics: 21.8, 24.1, 24.6, 26.2, 28.4, 35.2, 36.3 b. Number of riders in 8 cars: 1, 1, 1, 1, 1, 1, 4, 6 c. Diners at 10 restaurant tables: 1, 2, 2, 2, 3, 3, 4, 4, 4, 5
In a regional high school swim meet, women's times (in seconds) in the 200-yard freestyle ranged from 109.7 to 126.2. Estimate the standard deviation, using the Empirical Rule.
Find the original data value corresponding to each standardized z-score.a. Student GPAs: Bob's z-score z = + 1.71, μ = 2.98, σ = 0.36b. Weekly work hours: Sarah's z-scorez = + 1.18, μ = 21.6, σ = 7.1c. Bowling scores: Dave's z-scorez = – 1.35, μ = 150, σ = 40
CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays.(a) Use Excel or MegaStat to sort and standardize the data.(b) Based on the Empirical Rule, are there outliers? Unusual data values?(c) Compare the percent of observations that lie within
An executive's telephone log showed the lengths of 65 calls initiated during the last week of July.(a) Use Excel or MegaStat to sort and standardize the data.(b) Based on the standardized z-scores, are there outliers? Unusual data values?(c) Compare the percent of observations that lie within 1 and
Scores on an accounting exam ranged from 42 to 96 with quartiles Q1 = 61, Q2 = 77 and Q3 = 85. (a) Sketch a simple boxplot (5-number summary without fences) using a nicely scaled X-asis. (b) Describe its shape (skewed left, symmetric, skewed right).
In 2007, total compensation (in thousands of dollars) for 40 randomly chosen CEOs ranged from 790 to 192,920, with quartiles Q1 = 3,825, Q2 = 8,890, and Q3 = 17,948. (a) Sketch a simple boxplot (5-number summary without fences) using a nicely scaled X-axis. (b) Describe its shape (skewed left,
The Comer-Correr Taco Wagon is only open from 11:00 a.m. to 2:00 p.m. on Saturday. The owner kept track of the number of customers served on Saturday for 60 weeks.(a) Visually estimate the quartiles Q1 , Q2 , Q3 .(b) Approximately how many customers were served on the Customers busiest day? The
On San Martin Boulevard, embedded sensors kept track of the vehicle traffic count each hour for five weekdays, Monday through Friday between 6 a.m. and 8 p.m. (5 weeks 3 14 hours 5 70 observations).(a) Visually estimate the quartiles Q1, Q2, Q3.(b) Estimate x min Traffic and xmax.(c) Is the
CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays.(a) Use Excel to find the quartiles. What do they tell you?(b) Find the midhinge. What does it tell you?(c) Make a box plot and interpret it.
An executive's telephone log showed the lengths of 65 calls initiated during the last week of July.(a) Use Excel to find the quartiles. What do they tell you?(b) Find the midhinge. What does it tell you?(c) Make a box plot and interpret it.
Days on the market are shown for the 36 most recent home sales in the city of Sonando Hills.(a) Calculate the mean, median, and mode.(b) Is the distribution skewed? Explain.(c) Is the mode a useful measure of center for this data set?
For each X-Y data set (n = 12):(a) Make a scatter plot.(b) Find the sample correlation coefficient.(c) Is there a linear relationship between X and Y? If so, describe it.
Your laptop gets warm (even hot) when you place it on your lap because it is dissipating heat from its microprocessor and related components.(a) Use the information in the following table to make a scatter plot.(b) Describe the relationship between Microprocessor Speed and Power Dissipation.(c)
For a sample of (X, Y) data values, the covariance is 48.724, the standard deviation of X is 11.724, and the standard deviation of Y is 8.244.(a) Find the sample correlation coefficient.(b) What does the sample correlation coefficient suggest about the relationship between X and Y?(c) Why is the
(a) Make a scatter plot of the following data on X = home size and Y = selling price (thousands of dollars) for new homes (n = 20) in a suburb of an eastern city.(b) Find the sample correlation coefficient.(c) Is there a linear relationship between X and Y? If so, describe it.
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 5 6 top runners):9.87, 9.98, 10.02, 10.15, 10.36, 10.36b. Number of children (n 5 13 families):0, 1, 1, 2, 2, 2, 2, 2, 2,
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.
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 a diameter of 0.2761. Find the standardized
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 unusual?
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 =7b. Weekly grocery bill: James' z-score = –1.45, μ = $53, σ = $12c. Daily video game play time: Eric's z-score = – 0.79, μ = 4.00 hours, σ = 1.15 hours
Scores are shown for the most recent state civil service exam taken by 24 applicants for positions in law enforcement.(a) Calculate the mean, median, and mode.(b) Is the distribution skewed? Explain.(c) Is the mode a useful measure of center for this data set?
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 against Fairview.(b) By the Empirical Rule, was
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 about the distribution of the number of
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 or unusual data values?(f) Using the Empirical
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) Calculate the quartiles and midhinge. (c)
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 for this data set? Explain.(d) Is the
The U.S. Postal Service will ship a Priority Mail ® Large Flat Rate Box (120 3 120 3 5 1 / 2 0) anywhere in the United States for a fixed price, regardless of weight. The weights (ounces) of 20 randomly chosen boxes are shown below.(a) Find the mean, median, and mode.(b) Are the mean and median
A sample of size n 5 70 showed a skewness coefficient of 0.773 and a kurtosis coefficient of 1.277. What is the distribution's shape?
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 funds.(a) Calculate the mean and median for each sample.(b) Calculate the standard
Statistics students were asked to ll a one-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 to the one-cup line, spread the contents on a large plate, and count the raisins. The 13 students
The table below shows estimates of the total cost of repairs in four bumper tests (full frontal, front corner, full rear, rear corner) on 17 cars.(a) Calculate the mean and median.(b) Would you say the data are skewed?(c) Why is the mode not useful for these data? (Data are from Insurance Institute
Prof. Hardtack gave four Friday quizzes last semester in his 10-student senior tax accounting class.(a) Find the mean, median, and mode for each quiz.(b) Do these measures of center agree? Explain.(c) For each data set, note strengths or weaknesses of each statistic of center.(d) Are the data
Grace took a random sample of the number of steps per minute from the electronic readout of her aerobic climbing machine during a 1-hour workout.(a) Calculate the mean, median, and mode.(b) Which is the best measure of center? The worst? Why? (Data are from a project by Grace Obringer, MBA student.)
How much revenue does it take to maintain a cricket club? The following table shows annual income for 18 first-class clubs that engage in league play.(a) Calculate the mean and median.(b) Describe a "typical" cricket club's income. (Data are from The Economist 367, no. 8329 [June 21, 2003], p. 47.)
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. Compare the variability of these distributions. Which demand pattern has more relative variation? Explain.
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) Are there any outliers?
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 tell you about risk and return?
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 standard deviation of 15.8 percent. (a) Calculate
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 assumption of a normal, bell-shaped distribution
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 Empirical Rule to estimate the standard deviation.
At the Midlothian Independent Bank, a study shows that the mean ATM transaction takes 74 seconds, the median 63 seconds, and the mode 51 seconds. (a) Sketch the distribution, based on these statistics. (b) What factors might cause the distribution to be like this?
At the Eureka library, the mean time a book is checked out is 13 days, the median is 10 days, and the mode is 7 days. (a) Sketch the distribution, based on these statistics. (b) What factors might cause the distribution to be like this?
CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays.(a) Find the mean, median, and mode.(b) Do these measures of center agree? Explain.(c) Make a histogram or dot plot.(d) Are the data symmetric or skewed? If skewed, which direction?
On Professor Hardtack's last cost accounting exam, the mean score was 71, the median was 77, and the mode was 81. (a) Sketch the distribution, based on these statistics. (b) What factors might cause the distribution to be like this?
The median life span of a mouse is 118 weeks. (a) Would you expect the mean to be higher or lower than 118? (b) Would you expect the life spans of mice to be normally distributed? Explain.
A small suburban community agreed to purchase police services from the county sheriff's department. The newspaper said, "In the past, the charge for police protection from the Sheriff's Department has been based on the median cost of the salary, fringe benefits, etc. That is, the cost per deputy
A company's contractual "trigger" point for a union absenteeism penalty is a certain distance above the mean days missed by all workers. Now the company wants to switch the trigger to a certain number of days above the median days missed for all workers. (a) Visualize the distribution of missed
(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 statistics?(c) Now calculate the median for each
A random sample of individuals who led their own income taxes were asked how much time (hours) they spent preparing last year's federal income tax forms.(a) Estimate the mean.(b) Estimate the standard deviation.(c) Do you think the observations would be distributed uniformly within each interval?
This table shows the distribution of winning times in the Kentucky Derby (a horse race) over 80 years. Times are recorded to the nearest 1 / 5 second (e.g., 121.4).(a) From the grouped data, calculate the mean. Show your calculations clearly in a worksheet.(b) What additional information would you
The self-reported number of hours worked per week by 204 top executives is given below.(a) Estimate the mean, standard deviation, and coefficient of variation, using an Excel work- sheet to organize your calculations.(b) Do the unequal class sizes hamper your calculations? Why do you suppose that
On Friday night, the owner of Chez Pierre in downtown Chicago noted the amount spent for dinner for 28 four-person tables.(a) Find the mean, median, and mode.(b) Do these measures of center agree? Explain.(c) Make a histogram or dot plot.(d) Are the data symmetric or skewed? If skewed, which
How long does it take to y from Denver to Atlanta on Delta Airlines? The table below shows 56 observations on fight times (in minutes) for the first week of March 2005.(a) Use the grouped data formula to estimate the mean and standard deviation.(b) Using the un- grouped data (not shown), the
(a) Make an Excel scatter plot of X = 1990 assault rate per 100,000 population and Y = 2004 assault rate per 100,000 population for the 50 U.S. states.(b) Use Excel's =CORREL function to find the correlation coefficient.(c) What do the graph and correlation coefficient say about assault rates by
(a) Make an Excel scatter plot of X = airspeed (nautical miles per hour) and Y = cockpit noise level (decibels) for 61 aircraft fights.(b) Use Excel's =CORREL function to find the correlation coefficient.(c) What do the graph and correlation coefficient say about the relationship between airspeed
An executive's telephone log showed the lengths of 65 calls initiated during the last week of July.(a) Sort the data.(b) Find the mean, median, and mode.(c) Do the measures of center agree? Explain.(d) Are the data symmetric or skewed? If skewed, which direction?
A credit card customer at Barnes and Noble can use Visa (V), MasterCard (M ), or American Express (A). The merchandise may be books (B), electronic media (E), or other (O). (a) Enumerate the elementary events in the sample space describing a customer's purchase. (b) Would each elementary event be
Are these characteristics of a student at your university mutually exclusive or not? Explain. a. A = works 20 hours or more, B = majoring in accounting b. A = born in the United States, B = born in Canada c. A = owns a Toyota, B = owns a Honda
Are these events collectively exhaustive or not? Explain. a. A = college grad, B = some college, C = no college b. A = born in the United States, B = born in Canada, C = born in Mexico c. A = full-time student, B = part-time student, C = not enrolled as a student
Given P(A) = .40, P(B) = .50, and P(A ∩ B) = .05, find(a) P(A ∪ B),(b) P(A | B), and(c) P(B | A).(d) Sketch a Venn diagram.
Given P (A) = .70, P (B) = .30, and P (A ∩ B) 5 .00, find(a) P(A ∪ B) and(b) P(A | B).(c) Sketch a Venn diagram.
Suppose Samsung ships 21.7 percent of the liquid crystal displays (LCDs) in the world. Let S be the event that a randomly selected LCD was made by Samsung. Find (a) P(S), (b) P(S), (c) The odds in favor of event S, and (d) The odds against event S.
Suppose the probability of an IRS audit is 1.7 percent for U.S. taxpayers who le form 1040 and who earned $100,000 or more.(a) What are the odds that such a taxpayer will be audited?(b) What are the odds against such a taxpayer being audited?
List two mutually exclusive events that describe the possible outcomes of each situation. a. A pharmaceutical firm seeks FDA approval for a new drug. b. A baseball batter goes to bat. c. A woman has a mammogram test.
A survey asked tax accounting firms their business form (S = sole proprietorship, P = partnership, C = corporation) and type of risk insurance they carry (L = liability only, T = property loss only, B = both liability and property). (a) Enumerate the elementary events in the sample space. (b) Would
List more than two events (i.e., categorical events) that might describe the outcome of each situation. a. A student applies for admission to Oxnard University. b. A football quarterback throws a pass. c. A bank customer makes an ATM transaction.
Let S be the event that a randomly chosen female aged 1824 is a smoker. Let C be the event that a randomly chosen female aged 1824 is a Caucasian. Given P(S) = .246, P(C) = .830, and P(S ∩ C) = .232, find each probability and express the event in words.a. P(S).b. P(S ∪ C).c. P(S | C).d. P(S
Given P (A) = .40, P (B) = .50. If A and B are independent, find P (A ∩ B).
Given P(A) = .40, P(B) = .50, and P(A ∩ B) = .05.(a) Find P(A | B).(b) In this problem, are A and B independent? Explain.
Which pairs of events are independent?a. P(A) = .60, P(B) = .40, P(A ∩ B) = .24.b. P(A) = .90, P(B) = .20, P(A ∩ B) = .18.c. P(A) = .50, P(B) = .70, P(A ∩ B) = .25.
The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .18. The probability that a student has both cards is .03.(a) Find the probability that a student has either a Visa card or a MasterCard.(b) In this problem, are V and M
Bob sets two alarm clocks (battery-powered) to be sure he arises for his Monday 8:00 a.m. accounting exam. There is a 75 percent chance that either clock will wake Bob.(a) What is the probability that Bob will oversleep?(b) If Bob had three clocks, would he have a 99 percent chance of waking up?
A hospital's backup power system has three independent emergency electrical generators, each with uptime averaging 95 percent (some downtime is necessary for maintenance). Any of the generators can handle the hospital's power needs. Does the overall reliability of the backup power system meet the
Over 1,000 people try to climb Mt. Everest every year. Of those who try to climb Everest, 31 percent succeed. The probability that a climber is at least 60 years old is .04. The probability that a climber is at least 60 years old and succeeds in climbing Everest is .005.(a) Find the probability of
Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 80 percent order a soft drink, and 40 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Explain.
A baseball player bats either left-handed (L) or right-handed (R). The player either gets on base (B) or does not get on base (B). (a) Enumerate the elementary events in the sample space. (b) Would these elementary events be equally likely? Explain.
The contingency table below shows the results of a survey of online video viewing by age. Find the following probabilities or percentages:a. Probability that a viewer is aged 1834.b. Probability that a viewer prefers watching TV videos.c. Percentage of viewers who are 1834 and prefer watching
The contingency table below summarizes a survey of 1,000 bottled beverage consumers. Find the following probabilities or percentages:a. Probability that a consumer recycles beverage bottles.b. Probability that a consumer who lives in a state with a deposit law does not recycle.c. Percentage of
A survey of 158 introductory statistics students showed the following contingency table. Find each event probability.a. P(V) b. P(A) c. P(A ∩ V ) d. P(A ∪ V )e. P(A | V )f. P(V | A)
A survey of 156 introductory statistics students showed the following contingency table. Find each event probability.a. P(D)b. P(R) c. P(D ∩ R) d. P(D ∪ R)e. P(R | D)f. P(R | P)
This contingency table describes 200 business students. Find each probability and interpret it in words.a. P(A)b. P(M) c. P(A ∩ M )d. P(F ∩ S)e. P(A | M )f. P(A | F)g. P(F | S)h. P(E ∪ F)
The following contingency table shows average yield (rows) and average duration (columns) for 38 bond funds. For a randomly chosen bond fund, find the probability that:a. The bond fund is long duration.b. The bond fund has high yield.c. The bond fund has high yield given that it is of short
Of grocery shoppers who have a shopping cart, 70 percent pay by credit/debit card (event C1), 20 percent pay cash (event C2), and 10 percent pay by check (event C3). Of shoppers without a grocery cart, 50 percent pay by credit/debit card (event C1), 40 percent pay cash (event C2), and 10 percent
A study showed that 60 percent of The Wall Street Journal subscribers watch CNBC every day. Of these, 70 percent watch it outside the home. Only 20 percent of those who don't watch CNBC every day watch it outside the home. Let D be the event "watches CNBC daily" and O be the event "watches CNBC
A drug test for athletes has a 5 percent false positive rate and a 10 percent false negative rate. Of the athletes tested, 4 percent have actually been using the prohibited drug. If an athlete tests positive, what is the probability that the athlete has actually been using the prohibited drug?
A die is thrown (1, 2, 3, 4, 5, 6) and a coin is tossed (H, T). (a) Enumerate the elementary events in the sample space for the die/coin combination. (b) Are the elementary events equally likely? Explain.
Half of a set of the parts are manufactured by machine A and half by machine B. Four per- cent of all the parts are defective. Six percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. Explain
An airport gamma ray luggage scanner coupled with a neural net artificial intelligence program can detect a weapon in suitcases with a false positive rate of 2 percent and a false negative rate of 2 percent. Assume a .001 probability that a suitcase contains a weapon. If a suitcase triggers the
(a) Find 8! without a calculator. Show your work.(b) Use your calculator to nd 32!.(c) Which method would you use most often? Why?
In the Minnesota Northstar Cash Drawing you pick five different numbers between 1 and 31. What is the probability of picking the winning combination (order does not matter)?
American Express Business Travel uses a six-letter record locator number (RLN) for each client's trip (e.g., KEZLFS). (a) How many different RLNs can be created using capital letters (AZ)? (b) What if they allow any mixture of capital letters (AZ) and digits (09)? (c) What if they allow
At Oxnard University, a student ID consists of two letters (26 possibilities) followed by four digits (10 possibilities). (a) How many unique student IDs can be created? (b) Would one letter followed by three digits suffice for a university with 40,000 students? (c) Why is extra capacity in student

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