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business
business statistics

Questions and Answers of Business Statistics

Mendel’s peas. Gregor Mendel used garden peas in some of the experiments that revealed that inheritance operates randomly. The seed color of Mendel’s peas can be either green or yellow. Suppose
Models legitimate and not. A bridge deck contains 52 cards, four of each of the 13 face values ace, king, queen, jack, ten, nine, . . . , two. You deal a single card from such a deck and record the
An IQ test (optional). How high must a person score on the WAIS test to be in the top 10% of all scores? Use the information in Exercise III.14 and Table B to answer this question.
We like opinion polls (optional). Use the information in Exercise III.15 and Table B to find the probability that one sample misses the truth about the population by 4% or more. (This is the
An IQ test (optional). Use the information in Exercise III.14 and Table B to find the probability that a randomly chosen person has aWAIS score 112 or higher.
We like opinion polls. Are Americans interested in opinion polls about the major issues of the day? Suppose that 40% of all adults are very interested in such polls. (According to sample surveys that
An IQ test. TheWechsler Adult Intelligence Scale (WAIS) is a common IQ test for adults. The distribution of WAIS scores for persons over 16 years of age is approximately Normal with mean 100 and
Satisfaction with colleges. The National Center for Public Policy and Higher Education asked randomly chosen adults, “Are the colleges in your state doing an excellent, good, fair, or poor job, or
Choosing at random. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness,
Language study. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:Language: Spanish French German All
How much education? The 2008 Statistical Abstract gives this distribution of education for a randomly chosen American over 25 years old:Less than High school College, Associate’s Bachelor’s
Poker. Deal a five-card poker hand from a shuffled deck. The probabilities of several types of hand are approximately as follows:Hand: Worthless One pair Two pairs Better hands Probability: 0.50 0.42
Profit from a risky investment. Rotter Partners is planning a major investment. The amount of profit X is uncertain, but a probabilistic estimate gives the following distribution (in millions of
Dice. What is the expected number of spots observed in rolling a carefully balanced die once? (Hint: See pages 429–432.)
Course grades. Choose a student at random from the course described in Exercise III.2 and observe what grade that student earns (A = 4, B = 3, C =2, D = 1, F = 0).(a) What is the expected grade of a
Blood types. People with Type B blood can receive blood donations from other people with either Type B or Type O blood. Tyra has Type B blood. What is the probability that 2 or more of Tyra’s 6
Course grades. If you choose 5 students at random from all those who have taken the course described in Exercise III.2, what is the probability that all the students chosen got a B or better?
Blood types. Choose a person at random and record his or her blood type. Here are the probabilities for each blood type:Blood type: Type O Type A Type B Type AB Probability: 0.4 0.3 0.2 ?(a) What
Course grades. Choose a student at random from all who took Math 101 in recent years. The probabilities for the student’s grade are Grade: A B C D F Probability: 0.2 0.4 0.2 0.1 ?(a) What must be
What’s the probability? Open your local telephone directory to any page in the residential listing. Look at the last four digits of each telephone number, the digits that specify an individual
Web-based exercise. The Web abounds in applets that simulate various random phenomena. One amusing probability problem is named Buffon’s needle. Draw lines 1 inch apart on a piece of paper, then
Web-based exercise. The basketball player LeBron James makes about 70% of his free throws over an entire season. At the end of a game, an announcer states that “LeBron had a hot hand tonight. He
The multiplication rule. Here is another basic rule of probability: if several events are independent, the probability that all of the events happen is the product of their individual
The birthday problem. A famous example in probability theory shows that the probability that at least two people in a room have the same birthday is already greater than 1/2 when 23 people are in the
More on the airport van. Let’s continue the simulation of Exercise 19.19. You have a backup van, but it serves several stations. The probability that it is available to go to the airport at any one
A multiple-choice exam. Matt has lots of experience taking multiplechoice exams without doing much studying. He is about to take a quiz that has 10 multiple-choice questions, each with four possible
The airport van. Your company operates a van service from the airport to downtown hotels. Each van carries 7 passengers. Many passengers who reserve seats don’t show up—in fact, the probability
Playing craps. The game of craps is played with two dice. The player rolls both dice and wins immediately if the outcome (the sum of the faces) is 7 or 11. If the outcome is 2, 3, or 12, the player
Two warning systems. An airliner has two independent automatic systems that sound a warning if there is terrain ahead (that means the airplane is about to fly into a mountain). Neither system is
The Asian stochastic beetle. We can use simulation to examine the fate of populations of living creatures. Consider the Asian stochastic beetle.Females of this insect have the following pattern of
Gambling in ancient Rome. Tossing four astragali was the most popular game of chance in Roman times. Many throws of a present-day sheep’s astragalus show that the approximate probability
A better model for repeating an exam. A more realistic probability model for Elaine’s attempts to pass an exam in the previous exercise is as follows. On the first try she has probability 0.2 of
Repeating an exam. Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has probability 2/10 of passing on any one
Tonya’s free throws. Tonya makes 80% of her free throws in a long season. In a tournament game she shoots 5 free throws late in the game and misses 3 of them. The fans think she was nervous, but
LeBron’s free throws. The basketball player LeBron James makes about 70% of his free throws over an entire season. Take his probability of a success to be 0.7 on each shot. Using line 122 of Table
More on class rank. In Exercise 19.8 you explained how to simulate the high school class rank of a randomly chosen college student. The Random Foundation decides to offer 8 randomly chosen students
More on course grades. In Exercise 19.7 you explained how to simulate the grade of a randomly chosen student in a statistics course. Five students on the same floor of a dormitory are taking this
Class rank. Choose a college student at random and ask his or her class rank in high school. Probabilities for the outcomes are Top quarter but Top half but Bottom Class rank: Top 10% not top 10% not
Course grades. Choose a student at random from all who took beginning statistics at Upper Wabash Tech in recent years. The probabilities for the student’s grade are Grade: A B C D or F Probability:
Simulating an opinion poll. A Gallup Poll on Presidents Day 2008 interviewed a random sample of 1007 adult Americans. Those in the sample were asked which former president they would like to bring
Basic simulation. Use Table A to simulate the responses of 10 independently chosen adults in each of the four situations of Exercise 19.3.(a) For situation (a), use line 110.(b) For situation (b),
A small opinion poll. Suppose that 90% of a university’s students favor abolishing evening exams. You ask 10 students chosen at random. What is the probability that all 10 favor abolishing evening
Which party does it better? An opinion poll selects adult Americans at random and asks them, “Which political party, Democratic or Republican, do you think is better able to manage the economy?”
Selecting cards at random. In a standard deck of 52 cards, there are 13 spades, 13 hearts, 13 diamonds, and 13 clubs. Carry out a simulation to determine the probability that, when two cards are
Selecting cards at random. In a standard deck of 52 cards, there are 13 spades, 13 hearts, 13 diamonds, and 13 clubs. How would you assign digits for a simulation to determine the suit (spades,
Web-based exercise. One of the best ways to grasp the idea of probability is to watch the proportion of trials on which an outcome occurs gradually settle down at the outcome’s probability.
Web-based exercise. Search the Web to see if you can find an example of a misuse or misstatement of the law of averages. Explain why the statement you find is incorrect. (We found some examples by
What probability doesn’t say. The probability of a head in tossing a coin is 1/2. This means that as we make more tosses, the proportion of heads will eventually get close to 0.5. It does not mean
Reacting to risks. National newspapers such as USA Today and the New York Times carry many more stories about deaths from airplane crashes than about deaths from automobile crashes. Auto accidents
Reacting to risks. The probability of dying if you play high school football is about 10 per million each year you play. The risk of getting cancer from asbestos if you attend a school in which
An unenlightened gambler.(a) A gambler knows that red and black are equally likely to occur on each spin 392 CHAPTER 17 Thinking about Chance of a roulette wheel. He observes five consecutive reds
Snow coming. A meteorologist, predicting above-average snowfall this winter, says, “First, in looking at the past few winters, there has been belowaverage snowfall. Even though we are not supposed
The “law of averages.” The baseball player Ichiro Suzuki gets a hit about 1/3 of the time over an entire season. After he has failed to hit safely in nine straight at-bats, the TV commentator
In the long run. Probability works not by compensating for imbalances but by overwhelming them. Suppose that the first 10 tosses of a coin give 10 tails and that tosses after that are exactly half
Nash’s free throws. The basketball player Steve Nash is the all-time career free throw shooter among active players. He makes about 90% of his free throws. In today’s game, Nash misses his first
Surprising? You are getting to know your new roommate, assigned to you by the college. In the course of a long conversation, you find that both of you have sisters named Deborah. Should you be
Playing Pick 4. The Pick 4 games in many state lotteries announce a four-digit winning number each day. The winning number is essentially a fourdigit group from a table of random digits. You win if
Personal random numbers? Ask several of your friends (at least 10 people) to choose a four-digit number “at random.” How many of the numbers chosen start with 1 or 2? How many start with 8 or 9?
Personal probability? When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successful, before the Challenger disaster in January
Personal probability versus data. Give an example in which you would rely on a probability found as a long-term proportion from data on many trials. Give an example in which you would rely on your
Marital status. The probability that a randomly chosen 50-yearold woman is divorced is about 0.18. This probability is a long-run proportion based on all the millions of women aged 50. Let’s
Will you have an accident? The probability that a randomly chosen driver will be involved in an accident in the next year is about 0.2. This is based on the proportion of millions of drivers who have
Winning a baseball game. Over the period from 1967 to 2007 the champions of baseball’s two major leagues won 62% of their home games during the regular season. At the end of each season, the two
From words to probabilities. Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. (The probability is
Two pairs. You read in a book on poker that the probability of being dealt two pairs in a five-card poker hand is 1/21. Explain in simple language what this means.
Tossing a thumbtack. Toss a thumbtack on a hard surface 100 times.How many times did it land with the point up? What is the approximate probability of landing point up?
How many tosses to get a head? When we toss a penny, experience shows that the probability (long-term proportion) of a head is close to 1/2. Suppose now that we toss the penny repeatedly until we get
Random digits. The table of random digits (Table A) was produced by a random mechanism that gives each digit probability 0.1 of being a 0. What proportion of the first 200 digits in the table are 0s?
Pennies falling over. You may feel that it is obvious that the probability of a head in tossing a coin is about 1/2 because the coin has two faces. Such opinions are not always correct. The previous
Pennies spinning. Hold a penny upright on its edge under your forefinger on a hard surface, then snap it with your other forefinger so that it spins for some time before falling. Based on 50 spins,
Coin tossing and the law of averages. The author C. S. Lewis once wrote the following, referring to the law of averages: “If you tossed a coin a billion times, you could predict a nearly equal
Coin tossing and randomness. Toss a coin 10 times and record heads (H) or tails (T) on each toss. Which of these outcomes is most probable? Least probable?HTHTTHHTHT TTTTTHHHHH HHHHHHHHHH
Web-based exercise. Information about basketball players can be found at www.basketball-reference.com. Go to this Web site and find the percentage of three-point shots that Steve Nash has made in his
Web-based exercise. Most states have a lotto game that offers large prizes for choosing (say) 6 out of 51 numbers. If your state has a lotto game, find out what percentage of the money bet is
Casino winnings. What is a secret, at least to naive gamblers, is that in the real world a casino does much better than expected values suggest. In fact, casinos keep a bit over 20% of the money
A common expected value. Here is a common setting that we simulated in Chapter 19: there are a fixed number of independent trials with the same two outcomes and the same probabilities on each trial.
Repeating an exam. Exercise 19.14 (page 424) gives a model for up to three attempts at an exam in a self-paced course. In that exercise, you simulated 50 repetitions to estimate Elaine’s
A multiple-choice exam. Charlene takes a quiz with 10 multiplechoice questions, each with four answer choices. If she just guesses independently at each question, she has probability 0.25 of guessing
Play this game, please. OK, friends, we’ve got a little deal for you.We have a fair coin (heads and tails each have probability 1/2). Toss it twice.If two heads come up, you win right there. If you
We really want a girl. Example 4 estimates the expected number of children a couple will have if they keep going until they get a girl or until they have three children. Suppose that they set no
Course grades. The distribution of grades in a large statistics course is as follows:Grade: A B C D F Probability: 0.2 0.3 0.3 0.1 0.1 To calculate student grade point averages, grades are expressed
Family size. The Census Bureau gives this distribution for the number of people in American families in 2006:Family size: 2 3 4 5 6 7 Proportion: 0.45 0.23 0.19 0.09 0.03 0.02 Chapter 20 Exercises
Life insurance. You might sell insurance to a 21-year-old friend. The probability that a man aged 21 will die in the next year is about 0.0015. You decide to charge $250 for a policy that will pay
The Asian stochastic beetle again. In Exercise 20.12 you found the expected number of female offspring of the Asian stochastic beetle. Simulate the offspring of 100 beetles and find the mean number
An expected rip-off? A “psychic” runs the following ad in a magazine:Expecting a baby? Renowned psychic will tell you the sex of the unborn child from any photograph of the mother. Cost, $20.
The Asian stochastic beetle. We met this insect in Exercise 19.16(page 425). Females have this probability model for their number of female offspring:Offspring: 0 1 2 Probability: 0.2 0.3 0.5(a) What
Rolling two dice. Example 2 of Chapter 18 (page 398) gives a probability model for rolling two casino dice and recording the number of spots on each of the two up-faces. That example also shows how
Keno. Keno is a popular game in casinos. Balls numbered 1 to 80 are tumbled in a machine as the bets are placed, then 20 of the balls are chosen at random. Players select numbers by marking a card.
Estimating sales. Gain Communications sells aircraft communications units. Next year’s sales depend on market conditions that cannot be predicted exactly. Gain follows the modern practice of using
Making decisions. A six-sided die has two green and four red faces and is balanced so that each face is equally likely to come up. You must choose one of the following three sequences of colors:RGRRR
Making decisions. The psychologist Amos Tversky did many studies of our perception of chance behavior. In its obituary of Tversky, the New York Times cited the following example.(a) Tversky asked
More roulette. An American roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots.
More Pick 4. Just as with Pick 3 (Example 2), you can make more elaborate bets in Pick 4. In the $1 StraightBox (24-way) bet, if you choose 1234 you win $2604 if the randomly chosen winning number is
Pick 4. The Tri-State Daily Numbers Pick 4 is much like the Pick 3 game of Example 1.Winning numbers for both are reported on television and in local newspapers. You pay $0.50 and pick a four-digit
The numbers racket. Pick 3 lotteries (Example 1) copy the numbers racket, an illegal gambling operation common in the poorer areas of large cities.States usually justify their lotteries by donating a
Kobe Bryant’s three-point shooting. Kobe Bryant makes about 1/3 of the three-point shots that he attempts. On average, how many three-point shots must he take in a game before he makes his first
Number of children. The Census Bureau gives this distribution for the number of a family’s own children under the age of 18 in American families in 2006:Number of children: 0 1 2 3 4 Proportion:
Web-based exercise. You can compare the behavior of the mean and median by using the Mean and Median applet at the Statistics: Concepts and ControversiesWeb site, www.whfreeman.com/scc. Click to
Web-based exercise. Willie Mays is fourth on the career home run list, behind Barry Bonds, Hank Aaron, and Babe Ruth. You can find Willie Mays’s home run statistics at the Web site
What graph to draw? We now understand three kinds of graphs to display distributions of quantitative variables: histograms, stemplots, and boxplots.Give an example (just words, no data) of a

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