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Questions and Answers of Statistics

According to results from the Spine Patient Outcomes Research Trial, or SPORT, surgery for a painful, common back condition resulted in significantly reduced back pain and better physical function
Consider the following contingency table.a. Convert the contingency table into a joint probability table.b. What is the probability that A occurs?c. What is the probability that A and B occur?d.
Consider the following joint probability table.a. What is the probability that A occurs?b. What is the probability that B2 occurs?c. What is the probability that Ac and B4 occur?d. What is the
According to an online survey by Harris Interactive for job site CareerBuilder.com, more than half of IT (information technology) workers say they have fallen asleep at work ( InformationWeek ,
A recent poll asked 16- to 21-year-olds whether or not they are likely to serve in the U.S. military. The following table, cross-classified by gender and race, reports the percentage of those polled
A recent report suggests that business majors spend the least amount of time on course work than all other college students (The New York Times, November 17, 2011). A provost of a university decides
According to a Michigan State University researcher, Americans are becoming increasingly polarized on issues pertaining to the environment. (news.msu.edu, April 19, 2011). It is reported that 70% of
Merck & Co. conducted a study to test the promise of its experimental AIDS vaccine ( The Boston Globe , September 22, 2007). Volunteers in the study were all free of the human immunodeficiency virus
More and more households are struggling to pay utility bills given a shaky economy and high heating costs (The Wall Street Journal, February 14, 2008). Particularly hard hit are households with homes
The research team at a leading perfume company is trying to test the market for its newly introduced perfume. In particular the team wishes to look for gender and international differences in the
Let P (A) = 0.70, P (B | A) = 0.55, and P (B | Ac) = 0.10. Use a probability tree to calculate the following probabilities:a. P (Ac)b. P (A ∩ B) and P (Ac ∩ B)c. P (B)d. P (A | B)
Let P (B) = 0.60, P (A | B) = 0.80, and P (A | Bc) = 0.10. Calculate the following probabilities:a. P (Bc)b. P (A ∩ B) and P (A ∩ Bc)c. P (A)d. P (B | A)
Complete the following probabilitytable.
Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and B3. Complete the following probabilitytable.
Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 40% chance that she will fail the course if she does not have a tutor.With a
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed
The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater
According to a recent study, cell phones are the main medium for teenagers to stay connected with friends and family (CNN, March 19, 2012). It is estimated that 90% of older teens (aged 14 to 17) and
According to data from the National Health and Nutrition Examination Survey, 33% of white, 49.6% of black, 43% of Hispanic, and 8.9% of Asian women are obese. In a representative town, 48% of women
A crucial game of the Los Angeles Lakers basketball team depends on the health of their key player. According to his doctor’s report, there is a 40% chance that he will be fully it to play, a 30%
An analyst thinks that next year there is a 20% chance that the world economy will be good, a 50% chance that it will be neutral, and a 30% chance that it will be poor. She also predicts
According to a global survey of 4,400 parents of children between the ages of 14 to 17, 44% of parents spy on their teen’s Facebook account (msnbc.com, April 25, 2012).Assume that American parents
According to a recent study, cell phones, especially text messaging, is the main medium for teenagers to stay connected with friends and family (CNN, March 19, 2012). It is found that only 23% of
Henry Chow is a stockbroker working for Merrill Lynch. He knows from past experience that there is a 70% chance that his new client will want to include U.S. equity in her portfolio and a 50% chance
The following frequency distribution shows the ages of India€™s 40 richest individuals. One of these individuals is selected at random.a. What is the probability that the individual is
Anthony Papantonis, owner of Nauset Construction, is bidding on two projects, A and B. The probability that he wins project A is 0.40 and the probability that he wins project B is 0.25. Winning
Since the fall of 2008, millions of Americans have lost jobs due to the economic meltdown. A recent study shows that unemployment has not impacted males and females in the same way (Newsweek, April
How much you smile in your younger days can predict your later success in marriage (msnbc.com, April 16, 2009). The analysis is based on the success rate in marriage of people over age 65 and their
A professor of management has heard that eight students in his class of 40 have landed an internship for the summer. Suppose he runs into two of his students in the corridor.a. Find the probability
Wooden boxes are commonly used for the packaging and transportation of mangoes. A convenience store in Morganville, New Jersey, regularly buys mangoes from a wholesale dealer. For every shipment, the
According to the CGMA Economic Index, which measures executive sentiment across the world, 18% of all respondents expressed optimism about the global economy (www.aicpa.org, March 29, 2012).
At a local bar in a small Midwestern town, beer and wine are the only two alcoholic options. The manager noted that of all male customers who visited over the weekend, 150 ordered beer, 40 ordered
It has generally been believed that it is not feasible for men and women to be just friends (The New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are
A recent study in the Journal of the American Medical Association (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after
It has been reported that women end up unhappier than men later in life, even though they start out happier (Yahoo News, August 1, 2008). Early in life, women are more likely to fulfill their family
An analyst predicts that there is a 40% chance that the U.S. economy will perform well. If the U.S. economy performs well, then there is an 80% chance that Asian countries will also perform well. On
Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010).In a recent study it was reported that 22% of those who had depression went on to
According to data from the National Health and Nutrition Examination Survey, 36.5% of adult women and 26.6% of adult men are at a healthy weight. Suppose 50.52% of the adult population consists of
Suppose that 60% of the students do homework regularly.It is also known that 80% of students, who had been doing homework regularly, end up doing well in the course (get a grade of A or B). Only 20%
According to the Census’s Population Survey, the percentage of children with two parents at home is the highest for Asians and lowest for blacks (USA TODAY, February 26, 2009). It is reported that
Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of
You apply for a position at two firms. Let event A represent the outcome of getting an offer from the first firm and event B represent the outcome of getting an offer from the second firm.a. Explain
A recent study challenges the media narrative that foreclosures are dangerously widespread (New York Times, March 2, 2009). According to this study, 62% of all foreclosures were centered in only four
Consider the following discrete probability distribution.a. Is this a valid probability distribution? Explain.b. Graphically depict this probability distribution.c. What is the probability that the
Consider the following discrete probability distribution.a. Complete the probability distribution.b. Graphically depict the probability distribution and comment on the symmetry of the
Identify the possible values of the following random variables. Which of the random variables are discrete?a. The numerical grade a student receives in a course.b. The grade point average of a
Identify the possible values of the following random variables. Which of the random variables are discrete?a. The advertised size of a round Domino’s pizza.b. The actual size of a round Domino’s
India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the
A financial analyst creates the following probability distribution for the performance of an equity income mutual fund.a. Comment on the optimism or pessimism depicted in the analyst€™s
A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 55% chance that the player will miss both shots, a 25% chance that
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.a. Depict the above probability distribution graphically. Comment on whether or
Jane Wormley is a professor of management at a university.She expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5%
Fifty percent of the customers who go to Sears Auto Center for tires buy four tires and 30% buy two tires. Moreover, 18% buy fewer than two tires, with 5% buying none.a. What is the probability that
Calculate the mean, the variance, and the standard deviation of the following discrete probabilitydistribution.
Calculate the mean, the variance, and the standard deviation of the following discrete probabilitydistribution.
A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 5% chance
The manager of a publishing company plans to give a $20,000 bonus to the top 15 percent, $10,000 to the next 30 percent, and $5,000 to the next 10 percent of sales representatives. If the publishing
An electronics store sells additional warranties on its Blu-ray players. Twenty percent of the buyers buy the limited warranty for $25 and 5% buy the extended warranty for $60. What is the expected
You are considering buying insurance for your new laptop computer, which you have recently bought for $1,500. The insurance premium for three years is $80. Over the three-year period there is an 8%
Four years ago, Victor Consuelo purchased a very reliable automobile (as rated by a reputable consumer advocacy publication). His warranty has just expired, but the manufacturer has just offered him
You are considering two mutual funds for your investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table.You believe that the
Investment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly
Assume that X is a binomial random variable with n = 5 and p = 0.35. Calculate the following probabilities.a. P(X = 0)b. P(X = 1)c. P(X ≤ 1)
Assume that X is a binomial random variable with n = 6 and p = 0.68. Calculate the following probabilities.a. P(X = 5)b. P(X = 4)c. P(X ≥ 4)
Assume that X is a binomial random variable with n = 8 and p = 0.32. Calculate the following probabilities.a. P (3 < X < 5)b. P (3 < X ≤ 5)c. P (3 ≤ X ≤ 5)
Let the probability of success on a Bernoulli trial be 0.30. In five Bernoulli trials, what is the probability that there will be(a) 4 failures,(b) More than the expected number of failures?
Let X represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities.a. P(X ≤ 50)b. P(X = 40)c. P(X > 60)d. P(X ≥ 55)
Let X represent a binomial random variable with n = 200 and p = 0.77. Find the following probabilities.a. P (X ≤ 150)b. P (X > 160)c. P (155 ≤ X ≤ 165)d. P (X = 160)
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal , June 26, 2008).
At a local community college, 40% of students who enter the college as freshmen go on to graduate. Ten freshmen are randomly selected.a. What is the probability that none of them graduates from the
The percentage of Americans who have confidence in U.S. banks dropped to 23% in June 2010, which is far below the pre-recession level of 41% reported in June 2007 (gallup.com).a. What is the
In recent analyses of Census figures, one in four American counties has passed or is approaching the tipping point where black, Hispanic, and Asian children constitute a majority of the under-20
Approximately 76% of baby boomers aged 43 to 61 are still in the workforce (The Boston Globe, July 10, 2008). Six baby boomers are selected at random.a. What is the probability that exactly one of
Sikhism, a religion founded in the 15th century in India, is going through turmoil due to a rapid decline in the number of Sikh youths, who wear turbans (Washington Post, March 29,2009). The tedious
According to the U.S. Census, roughly half of all marriages in the United States end in divorce. Researchers from leading universities have shown that the emotions aroused by one person’s divorce
Sixty percent of a firm’s employees are men. Suppose four of the firm’s employees are randomly selected.a. What is more likely, finding three men and one woman or two men and two women?b. Do you
The principal of an architecture firm tells her client that there is at least a 50% chance of having an acceptable design by the end of the week. She knows that there is only a 25% chance that any
Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.a. What is the probability that no more than four of the college
At the University of Notre Dame Mendoza College of Business, 40% of the students seeking a master’s degree specialize in finance (Kiplinger’s Personal 0Finance, March2009). Twenty master’s
The Washington, D.C., region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure during the one-year period ending inFebruary 2008 (The Washington
Assume that X is a Poisson random variable with µ = 1.5. Calculate the following probabilities.a. P(X = 1)b. P(X = 2)c. P(X ≥ 2)
Assume that X is a Poisson random variable with µ = 4. Calculate the following probabilities.a. P(X = 4)b. P(X = 2)c. P(X ≤ 1)
Let the mean success rate of a Poisson process be 8 successes per hour.a. Find the expected number of successes in a half-hour period.b. Find the probability of at least 2 successes in a given
Assume that X is a Poisson random variable with µ = 15. Calculate the following probabilities.a. P(X ≤ 10)b. P(X = 13)c. P(X > 15)d. P(12 ≤ X ≤ 18)
Assume that X is a Poisson random variable with µ = 20. Calculate the following probabilities.a. P(X < 14)b. P(X ≥ 20)c. P(X = 25)d. P(18 ≤ X ≤ 23)
A textile manufacturing process finds that on average, 2 laws occur per every 50 yards of material produced.a. What is the probability of exactly 2 laws in a 50-yard piece of material?b. What is the
A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour.a. Find the probability that 2 cars arrive during a specified one-minute period.b. Find the
Airline travelers should be ready to be more flexible as airlines once again cancel thousands of lights this summer.The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls
Motorists arrive at a Gulf gas station at the rate of two per minute during morning hours.a. What is the probability that more than two motorists will arrive at the Gulf gas station during a
According to a recent government report, the aging of the U.S. population is translating into many more visits to doctors’ offices and hospitals (USA Today, August 7, 2008). It is estimated that an
In the fiscal year that ended September 30, 2008, there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission, an increase of 29% from the previous year (The
According to Nielsen, the average teenager sends 3,339 texts per month (CNN, October 15, 2010).a. Find the probability that an average teenager sends more than 1,000 texts per week.b. Find the
Assume that X is a hyper-geometric random variable with N = 25, S = 3, and n = 4. Calculate the following probabilities.a. P(X = 0)b. P(X = 1)c. P(X ≤ 1)
Assume that X is a hyper-geometric random variable with N = 15, S = 4, and n = 3. Calculate the following probabilities.a. P(X = 1)b. P(X = 2)c. P(X ≥ 2)
Compute the probability of no success in a random sample of three items obtained from a population of 12 items that contains two successes. What are the expected number and the standard deviation
(Use computer) Assume that X is a hyper-geometric random variable with N = 50, S = 20, and n = 5. Calculate the following probabilities.a. P(X = 2)b. P(X ≥ 2)c. P(X ≤ 3)
Compute the probability of at least eight successes in a random sample of 20 items obtained from a population of 100 items that contains 25 successes. What are the expected number and the standard
Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the
Many programming teams work independently at a large software company. The management has been putting pressure on these teams to finish a project on time. The company currently has 18 large
David Barnes and his fiance´e Valerie Shah are visiting Hawaii. There are 20 guests registered for orientation. It is announced that 12 randomly selected registered guests will receive a free lesson

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