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Questions and Answers of Business Statistics

Consumer Reports gave the following mileage ratings (in miles per gallon) for seven midsize hybrid 2016 model cars (consumerreports.org/cro/cars /new-cars/hybrids evs/ratings-reliability/ratings
The authors of the paper “Driving Performance While Using a Mobile Phone: A Simulation Study of Greek Professional Drivers” (Transportation Research Part F [2016]: 164–170) describe a study to
The paper referenced in the previous exercise also reported that for a representative sample of 68 second-year students at the university, the sample mean procrastination score was 41.0 and the
Students in a representative sample of 65 first-year students selected from a large university in England participated in a study of academic procrastination (“Study Goals and Procrastination
The paper “The Effects of Adolescent Volunteer Activities on the Perception of Local Society and Community Spirit Mediated by Self-Conception” (Advanced Science and Technology Letters [2016]:
USA TODAY reported that the average amount of money spent on coffee drinks each month is $78.00 (USA TODAY Snapshot, November 4, 2016).a. Suppose that this estimate was based on a representative
In 2010, the online security firm Symantec estimated that 63% of computer users don’t change their passwords very often (cnet.com/news/survey-63-dont -change passwords-very-often, retrieved
Based on survey of a representative sample of 1000 adult Americans, YouGov estimated that the proportion of adult Americans who have less than $1000 in savings is 0.430 (“People More Likely to Save
The article “Most Americans Don’t Understand the Cloud, But They Should” (foxbusiness.com, October 17, 2016, retrieved November 12, 2016) reported that in a sample of 1000 people, 22% said they
In 2010, the National Football League adopted new rules designed to limit head injuries. In a survey conducted in 2015 by the Harris Poll, 1216 of 2096 adults indicated that they were football fans
Business Insider reported that a study commissioned by eBay motors found that nearly 40% of millennials who drive a car that is more than 5 years old have named their cars (“Millennials Have an Odd
Each person in a random sample of 20 students at a particular university was asked whether he or she is registered to vote. The responses (R = registered, N = not registered) are given here:R R N R N
The USA TODAY Snapshot titled “Have a Nice Trip” (USA TODAY, November 17, 2015) summarized data from a survey of 1000 U.S. adults who had traveled by air at least once in the previous year. The
USA TODAY reported that the proportion of Americans who prefer cheese on their burgers is 0.84 (USA TODAY, September 7, 2016). This estimate was based on a survey of a representative sample of 1000
The report “Job Seeker Nation Study 2016” (jobvite .com/wp-content/uploads/2016/03/Jobvite _Jobseeker_Nation_2016.pdf, retrieved May 6, 2017) summarized a survey of 2305 working adults. The
The USA TODAY Snapshot titled “Baby’s First Photo Reveal” (USA TODAY, October 17, 2014) summarized data from a survey of 1001 mothers with children under the age of 2. The Snapshot includes the
The Princeton Review 2016 College Hopes and Worries Survey Report (princetonreview.com/cms -content/final_cohowo2016survrpt.pdf, retrieved May 6, 2017) reported that 31% of students applying to
The article “Most Dog Owners Take More Pictures of Their Pet Than Their Spouse” (August 22,2016, news.fastcompany.com/most-dog-owners -take-more-pictures-of their-pet-than-their
The USA TODAY Snapshot titled “Big Bang Theory” (USA TODAY, October 14, 2016) summarized data from a sample of 1003 American parents of children age 6 to 11. It reported that 53% of these parents
The report “Parents, Teens and Digital Monitoring” (Pew Research Center, January 7, 2016, pewinternet.org/2016/01/07/parents-teens-and-digital -monitoring, retrieved April 4, 2018) reported
The USA TODAY Snapshot titled “Social Media Jeopardizing Your Job?” (USA TODAY, November 12, 2014) summarized data from a survey of 1855 recruiters and human resource professionals. The Snapshot
The authors of the paper ?Influence of Biofeedback Weight Bearing Training in Sit to Stand to Sit and the Limits of Stability on Stroke Patients? (The Journal of Physical Therapy Science [2016]:
The report “The 2016 Consumer Financial Literacy Survey” (The National Foundation for Credit Counseling (nfcc.org, retrieved October 28, 2016) summarized data from a representative sample of 1668
Let x1, x2, . . . , x100 denote the actual weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 50 pounds
The article “Fewer Americans Are Reading, But Don’t Blame the Millennials” (Los Angeles Times, October 9, 2016) indicates that 80% of millennials (those age 18 to 29) have read a book in the
The U.S. Census Bureau reported that in 2015, the proportion of adult Americans age 25 and older who have a bachelor’s degree or higher is 0.325 (“Educational Attainment in the United States:
The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x)
Kyle and Lygia are going to play a series of Trivial Pursuit games. The first person to win four games will be declared the winner. Suppose that outcomes of successive games are independent and that
Simulate sampling from the population of Exercise 8.7 by using four slips of paper individually marked 1, 2, 3, and 4. Select a sample of size 2 without replacement, and calculate x. Repeat this
Select 10 additional random samples of size 5 from the population of 20 students given in Example 8.1, and calculate the mean amount spent on books for each of the 10 samples. Are the x? values
Consider a population consisting of the following five values, which represent the number of video downloads during the academic year for each of five housemates:8 14 16
Suppose there are approximately 40,000 travel agencies in the United States, of which 11,000 are members of the American Society of Travel Agents (ASTA).a. If x is the number of ASTA members among
Four people—a, b, c, and d—are waiting to give blood. Of these four, a and b have type AB blood, whereas c and d do not. An emergency call has just come in for some type AB blood. If blood
Flashlight bulbs manufactured by a certain company are sometimes defective.a. If 5% of all such bulbs are defective, could the techniques of this section be used to approximate the probability that
Consider the information on the MENT test given in the previous exercise.a. The exact binomial probability of a score of 42 or less for someone who is not faking the test (p = 0.96) isp(x ≤ 42) =
Symptom validity tests (SVTs) are sometimes used to confirm diagnosis of psychiatric disorders. The paper “Developing a Symptom Validity Test for Post-Traumatic Stress Disorder: Application of the
For the binomial distribution described in the previous exercise, approximate the following probabilities using the normal approximation with the continuity correction.a. P(25 ≤ x ≤ 40)b. P(25
Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and σ = √np(1 - p) = 3.464. Approximate the following probabilities using the normal approximation with the
The figure on the next page appeared in the paper ?EDTA-Extractable Copper, Zinc, and Manganese in Soils of the Canterbury Plains? (New Zealand Journal of Agricultural Research [1984]: 207?217). A
The following normal probability plot was constructed using data on the price of seven 2015 Honda Accords with automatic transmissions that were listed for sale within 25 miles of the zip code 19383
Purchases made at small “corner stores” were studied by the authors of the paper “Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner
The article “New York City’s Graffiti-Removal Response Time Rises” (The Wall Street Journal,September 16, 2016, wsj.com/articles/new-york -citys-graffiti-removal response-time-rises
Determine each of the following areas under the standard normal (z) curve:a. To the right of 0b. To the right of 25c. Between 21.6 and 2.5d. To the left of 0.23
Suppose that 90% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of
Suppose that the probability is 0.1 that any given citrus tree will show measurable damage when the temperature falls to 308F.a. If the temperature does drop to 308F, what is the expected number of
Women’s Health Magazine surveyed 1187 readers to find out how often people wash their sheets (womenshealthmag.com/health/dirty-sheets, March 26, 2015, retrieved May 2, 2017). They found that even
Information Security Buzz provides news for the information security community. In an article published on September 24, 2016, it reported that based on a large international survey of Internet
CBS News reported that 4% of adult Americans have a food allergy (June 1, 2017, cbsnews.com /news/food-allergies-in-america-new-report -shellfish-peanut-dairy, retrieved March 25, 2018).Consider
Consider the random variables xR and xB defined in the previous exercise.a. Suppose that you are offered a choice of the following two games:Game 1: Pay $7 to play, and you win y1 dollars, where y1 =
Consider a game in which a red die and a blue die are rolled. Let xR denote the value showing on the uppermost face of the red die, and define xB similarly for the blue die. a. The probability
A multiple-choice exam consists of 50 questions. Each question has five choices, of which only one is correct. Suppose that the total score on the exam is calculated as where x1 = number of correct
To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and standard
The paper “Examining Communication- and Media- Based Recreational Sedentary Behaviors Among Canadian Youth: Results from the COMPASS Study” (Preventive Medicine [2015]: 74–80) estimated that
The events E and Ti are defined as E = the event that someone who is out of work and actively looking for work will find a job within the next month and Ti = the event that someone who is currently
An author has written a book and submitted it to a publisher. The publisher offers to print the book and gives the author the choice between a flat payment of $10,000 and a royalty plan. Under the
Refer to the information given in Exercise 7.39. a. Calculate the mean and variance of z 5 total number of vehicles (cars and buses) on the ferry. b. Calculate the mean and variance of w 5 total
Refer to the information given in Exercise 7.39. a. Calculate the mean and variance of the total amount of money collected in tolls from cars. b. Calculate the mean and variance of the total amount
Exercise 7.8 gave the following probability distribution for x = the number of courses for which a randomly selected student at a certain university is registered: For this probability
Referring to the previous exercise, use the result of Part (a) along with the fact that a carton contains 12 eggs to determine the mean value of z = the number of unbroken eggs. z can be written as a
Consider selecting a household in rural Thailand at random. Define the random variable x to bex = number of individuals living in the selected householdBased on information in an article that
The density curve for the random variable w (the sum of two wait times) is given in the previous exercise. What is the probability that w is between 10 and 30? It might be easier first to find the
The article “Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes” (12th International Conference on Applications of Statistics and Probability in Civil Engineering,
The accompanying data on x = student-teacher ratio for a random sample of 25 high schools in Maine selected from a population of 85 high schools are consistent with summary values for the state of
Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of the components are defect-free. Components are independently
Of all airline flight requests received by a certain discount ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Define the random variable x to be the number
Simulate the chance experiment described in the previous exercise using five slips of paper, with two marked defective and three marked not defective.Place the slips in a box, mix them well, and draw
Refer to the previous exercise. Suppose that because of the high rate of false-positives for the drug test, Mumble.com has instituted a mandatory independent second test for those who test positive
Suppose that a new Internet company Mumble .com requires all employees to take a drug test. Mumble .com can afford only the inexpensive drug test—the one with a 5% false-positive rate and a 10%
According to a study conducted by a risk assessment firm (Associated Press, December 8, 2005), drivers residing within 1 mile of a restaurant are 30% more likely to be in an accident in a given
The Cedar Rapids Gazette (November 20, 1999) reported the following information on compliance with child restraint laws for cities in Iowa: a. Use the information provided to estimate the following
The article “Doctors Misdiagnose More Women, Blacks” (San Luis Obispo Tribune, April 20, 2000) gave the following information, which is based on a large study of more than 10,000 patients treated
Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 a.m. A mailorder catalog company ships 30% of its overnight packages using service 1 and 70% using
A person stands at the corner marked A of the square pictured in Exercise 7.4 and tosses a coin. If it lands heads up, the person moves one corner clockwise, to B. If the coin lands tails up, the
Beverly is building a fireplace. She is using handmade decorative 8-inch bricks for the bottom row of the fireplace. Although the bricks are advertised as 8-inch bricks, the actual length of a brick
A point is randomly selected on the surface of a lake that has a maximum depth of 100 feet. Let y be the depth of the lake at the randomly chosen point.a. What are possible values of y?b. Is y
The following quote is from USA TODAY (January 21, 2010):Most Americans think the Census is important, and the majority say they will participate in the count this spring— although Hispanics,
A point is randomly selected from the interior of the square pictured. Let x denote the distance from the lower left-hand corner A of the square to the selected point.? a. What are possible values
Suppose that a box contains 25 light bulbs, of which 20 are good and the other 5 are defective. Consider randomly selecting three bulbs without replacement.Let E denote the event that the first bulb
Refer to Exercise 6.116, but now suppose that two viewers are randomly selected (without replacement). Let R1 and R2 denote the events that the first and second individuals, respectively, watched an
A theater complex is currently showing four R-rated movies, three PG-13 movies, two PG movies, and one G movie. The following table gives the number of people at the first showing of each movie on a
The general addition rule for three events states that A new magazine publishes columns entitled ?Art? (A), ?Books? (B), and ?Cinema? (C). Suppose that 14% of all subscribers read A23% read B 37%
In a school machine shop, 60% of all machine breakdowns occur on lathes and 15% occur on drill presses. Let E denote the event that the next machine breakdown is on a lathe, and let F denote the
A study of the impact of seeking a second opinion about a medical condition is described in the paper “Evaluation of Outcomes from a National Patient-Initiated Second Opinion Program” (The
The following table summarizing data on smoking status and age group is consistent with summary quantities obtained in a Gallup Poll published in the online article ?In U.S., Young Adults? Cigarette
The article “Obesity, Smoking Damage U.S. Economy,” which appeared in the Gallup Online Business Journal (gallup.com, September 7, 2016, retrieved April 25, 2017), reported that based on a large
False positive results are not uncommon with mammograms, a test used to screen for breast cancer. For a woman who has a positive mammogram, the probability that she actually has breast cancer is less
Four students must work together on a group project. They decide that each will take responsibility for a particular part of the project, as follows: Because of the way the tasks have been divided,
On April 1, 2010, the Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table given below are obtained for four counties in one
The report ?Airline Quality Rating 2016? (airlinequalityrating.com/reports/2016_AQR_Final .pdf, retrieved April 25, 2017) provides an overview of the complaints about airlines received by the U.S.
The paper referenced in the previous exercise also included data for a second radiologist, Radiologist 2. Based on the data from the previous exercise for Radiologist 1 and the data in the
Radiologists are often asked to predict the sex of a baby from ultrasound images made during pregnancy. The authors of the paper ?The Use of Three Dimensional Ultrasound for Fetal Gender
The article “U.S. Investors Split Between Digital and Traditional Banking” (gallup.com, August 5, 2016, retrieved April 25, 2017) summarized data from a Gallup survey of a random sample of 1019
Suppose that we define the following events:C = event that a randomly selected driver is observed to be using a cell phoneA = event that a randomly selected driver is observed driving a passenger
Refer to the information given in the previous exercise about customers of a large cable company.a. Suppose two customers are to be selected at random. Would it be reasonable to consider the events
Let F denote the event that a randomly selected registered voter in a certain city has signed a petition to recall the mayor. Also, let E denote the event that the randomly selected registered voter
A university has 10 vehicles available for use by faculty and staff. Six of these are vans and four are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two
Refer to the previous exercise. Suppose now that for a probability question, 100 answers are submitted, of which 50 are correct. Calculate the probabilities in Parts (a) and (b) of the previous
The National Public Radio show Car Talk used to have a feature called “The Puzzler.” Listeners were asked to send in answers to some puzzling questions—usually about cars but sometimes about
A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small (S), medium (M), and large (L). The proportions of the two brands and of the three sizes
Consider the following events:T = event that a randomly selected adult trusts credit card companies to safeguard his or her personal dataM = event that a randomly selected adult is between the ages

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