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Understanding Basic Statistics 7th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Critical Thinking On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the fi rst toss, are you guaranteed to get tails on the second toss? Explain.
Critical Thinking(a) Explain why 0.41 cannot be the probability of some event.(b) Explain why 1.21 cannot be the probability of some event.(c) Explain why 120% cannot be the probability of some event.(d) Can the number 0.56 be the probability of an event? Explain.
Probability Estimate: Wiggle Your Ears Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can
Probability Estimate: Raise One Eyebrow Can you raise one eyebrow at a time?Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can raise one eyebrow at a time. How can your result be thought of as an estimate for the probability that a person
Myers–Briggs: Personality Types Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defi ned according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an
General: Roll a Die(a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?(b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to
Psychology: Creativity When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information:(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate
Expand Your Knowledge: Odds in Favor Sometimes probability statements are expressed in terms of odds.The odds in favor of an event A are the ratio P A P not A 5P A P Ac .For instance, if P A 5 0.60, then P Ac 5 0.40 and the odds in favor of A are 0.60 0.40 56 45 32, written as 3 to 2 or 3:2(a) Show
Expand Your Knowledge: Odds Against Betting odds are usually stated against the event happening (against winning).The odds against event W are the ratio P not W P W 5P Wc P W.In horse racing, the betting odds are based on the probability that the horse does not win.(a) Show that if we are given the
Business: Customers John runs a computer software store. Yesterday he counted 127 people who walked by his store, 58 of whom came into the store.Of the 58, only 25 bought something in the store.(a) Estimate the probability that a person who walks by the store will enter the store.(b) Estimate the
Statistical Literacy If two events are mutually exclusive, can they occur concurrently?Explain.
Statistical Literacy If two events A and B are independent and you know that P A 5 0.3, what is the value of P A | B ?
Basic Computation: Addition Rule Given P A 5 0.3 and P B 5 0.4:(a) If A and B are mutually exclusive events, compute P(A or B).(b) If P A and B 5 0.1, compute P A or B .
Basic Computation: Addition Rule Given P A 5 0.7 and P B 5 0.4:(a) Can events A and B be mutually exclusive? Explain.(b) If P A and B 5 0.2, compute P(A or B).
Basic Computation: Multiplication Rule Given P A 5 0.2 and P B 5 0.4:(a) If A and B are independent events, compute P(A and B).(b) If P A | B 5 0.1, compute P(A and B).
Basic Computation: Multiplication Rule Given P A 5 0.7 and P B 5 0.8:(a) If A and B, are independent events, compute P(A and B).(b) If P B | A 5 0.9, compute P(A and B).
Basic Computations: Rules of Probability Given P A 5 0.2, P B 5 0.5, P A | B 5 0.3:(a) Compute P(A and B).(b) Compute P(A or B).
Basic Computation: Rules of Probability Given P Ac 5 0.8, P B 5 0.3, P B | A 5 0.2:(a) Compute P(A and B).(b) Compute P(A or B).
Critical Thinking Lisa is making up questions for a small quiz on probability.She assigns these probabilities: P(A) 5 0.3, P(B) 5 0.3, P(A and B) = 0.4.What is wrong with these probability assignments?
Critical Thinking Greg made up another question for a small quiz. He assigns the probabilities P(A) 5 0.6, P(B) 5 0.7, P(A | B) 5 0.1 and asks for the probability P(A or B). What is wrong with the probability assignments?
Critical Thinking Suppose two events A and B are mutually exclusive, with P A ? 0 and P B ? 0.By working through the following steps, you’ll see why two mutually exclusive events are not independent.(a) For mutually exclusive events, can event A occur if event B has occurred?What is the value of
Critical Thinking Suppose two events A and B are independent, with P A ? 0 and P B ? 0.By working through the following steps, you’ll see why two independent events are not mutually exclusive.(a) What formula is used to compute P(A and B)? Is P A and B ? 0? Explain.(b) Using the information from
Critical Thinking Consider the following events for a driver selected at random from the general population:A 5 driver is under 25 years old B 5 driver has received a speeding ticket Translate each of the following phrases into symbols.(a) The probability the driver has received a speeding ticket
Critical Thinking Consider the following events for a college student selected at random:A 5 student is female B 5 student is majoring in business Translate each of the following phrases into symbols.(a) The probability the student is male or is majoring in business(b) The probability a female
General: Candy Colors M&M plain candies come in various colors.According to the M&M/Mars Department of Consumer Affairs (link to the Mars company web site from the Brase/Brase statistics site at http://www.cengagebrain.com, the distribution of colors for plain M&M candies is Color Purple Yellow Red
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) Are the outcomes on the dice independent?(b) Find P(5 on green die and 3 on red die).(c) Find P(3 on green die and 5 on red die).(d) Find P((5 on green die and 3 on red die) or (3 on green die and 5 on red die)).
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) Are the outcomes on the dice independent?(b) Find P(1 on green die and 2 on red die).(c) Find P(2 on green die and 1 on red die).(d) Find P((1 on green die and 2 on red die) or (2 on green die and 1 on red die)).
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) What is the probability of getting a sum of 6?(b) What is the probability of getting a sum of 4?(c) What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive?
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) What is the probability of getting a sum of 7?(b) What is the probability of getting a sum of 11?(c) What is the probability of getting a sum of 7 or 11? Are these outcomes mutually exclusive?
General: Deck of Cards You draw two cards from a standard deck of 52 cards without replacing the fi rst one before drawing the second.(a) Are the outcomes on the two cards independent? Why?(b) Find P(Ace on 1st card and King on 2nd).(c) Find P(King on 1st card and Ace on 2nd).(d) Find the
General: Deck of Cards You draw two cards from a standard deck of 52 cards without replacing the fi rst one before drawing the second.(a) Are the outcomes on the two cards independent? Why?(b) Find P(3 on 1st card and 10 on 2nd).(c) Find P(10 on 1st card and 3 on 2nd).(d) Find the probability of
General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the fi rst one back and reshuffl e the deck.(a) Are the outcomes on the two cards independent? Why?(b) Find P(Ace on 1st card and King on 2nd).(c) Find P(King on 1st card and Ace
General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the fi rst one back and reshuffl e the deck.(a) Are the outcomes on the two cards independent? Why?(b) Find P(3 on 1st card and 10 on 2nd).(c) Find P(10 on 1st card and 3 on
Marketing: Toys USA Today gave the information shown in the table about ages of children receiving toys. The percentages represent all toys sold.What is the probability that a toy is purchased for someone(a) 6 years old or older?(b) 12 years old or younger?(c) between 6 and 12 years old?(d) between
Survey: Lung/Heart In an article titled “Diagnostic accuracy of fever as a measure of postoperative pulmonary complications” (Heart Lung, Vol. 10, No.1, p. 61), J. Roberts and colleagues discuss using a fever of 38C or higher as a diagnostic indicator of postoperative atelectasis (collapse of
Statistical Literacy What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate?
Statistical Literacy Consider a series of events. How does a tree diagram help you list all the possible outcomes of a series of events? How can you use a tree diagram to determine the total number of outcomes of a series of events?
Critical Thinking For each of the following situations, explain why the combinations rule or the permutations rule should be used.(a) Determine the number of different groups of 5 items that can be selected from 12 distinct items.(b) Determine the number of different arrangements of 5 items that
Critical Thinking You need to know the number of different arrangements possible for fi ve distinct letters. You decide to use the permutations rule, but your friend tells you to use 5!. Who is correct? Explain.
Tree Diagram(a) Draw a tree diagram to display all the possible head–tail sequences that can occur when you fl ip a coin three times.(b) How many sequences contain exactly two heads?(c) Probability Extension Assuming the sequences are all equally likely, what is the probability that you will get
Tree Diagram(a) Draw a tree diagram to display all the possible outcomes that can occur when you fl ip a coin and then toss a die.(b) How many outcomes contain a head and a number greater than 4?(c) Probability Extension Assuming the outcomes displayed in the tree diagram are all equally likely,
Tree Diagram There are six balls in an urn. They are identical except for color. Two are red, three are blue, and one is yellow. You are to draw a ball from the urn, note its color, and set it aside. Then you are to draw another ball from the urn and note its color.(a) Make a tree diagram to show
Tree Diagram(a) Make a tree diagram to show all the possible sequences of answers for three multiple-choice questions, each with four possible responses.(b) Probability Extension Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the
Multiplication Rule Four wires (red, green, blue, and yellow) need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the
Multiplication Rule A sales representative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order
Counting: Agriculture Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has four fertilizer types, three temperature zones, and three water treatments to test.
Counting: Outcomes You toss a pair of dice.(a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.)(b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die?(c) Probability
Counting: Hiring There are three nursing positions to be fi lled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor, and position 3 is the nursing coordinator position. There are 15 candidates qualifi ed for all three of the positions. Determine
Counting: Lottery In the Cash Now lottery game there are 10 fi nalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The fi rst prize is $1 million, the second prize is $100,000, and the third prize is $10,000. Determine the total number of
Counting: Sports The University of Montana ski team has fi ve entrants in a men’s downhill ski event. The coach would like the fi rst, second, and third places to go to the team members. In how many ways can the fi ve team entrants achieve fi rst, second, and third places?
Counting: Sales During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of 3 free software packages.There are 10 different software packages from which to select. How many different groups of software packages can be selected?
Counting: Hiring There are 15 qualifi ed applicants for 5 trainee positions in a fast-food management program. How many different groups of trainees can be selected?
Counting: Grading One professor grades homework by randomly choosing 5 out of 12 homework problems to grade.(a) How many different groups of 5 problems can be chosen from the 12 problems?(b) Probability Extension Jerry did only 5 problems of one assignment. What is the probability that the problems
Counting: Hiring The qualifi ed applicant pool for six management trainee positions consists of seven women and fi ve men.(a) How many different groups of applicants can be selected for the positions?(b) How many different groups of trainees would consist entirely of women?(c) Probability Extension
Counting: Powerball The Viewpoint of this section, on page 229, describes how the lottery game of Powerball is played.(a) The fi rst step is to select fi ve distinct whole numbers between 1 and 59.Order is not important. Use the appropriate counting rule to determine the number of ways groups of fi
The number need not be distinct from numbers chosen for the fi rst fi ve described in part (a). Use the appropriate counting rule to determine the number of possible distinct outcomes for the fi rst fi ve numbers, chosen as described in part (a) together with the Powerball number.Note: The
Statistical Literacy If two events A and B are mutually exclusive, what is the value of P(A and B)?
Statistical Literacy If two events A and B are independent, how do the probabilities P(A) and P A | B compare?
Critical Thinking You are given the information that P A 5 0.30 and P B 5 0.40.(a) Do you have enough information to compute P(A or B)? Explain.(b) If you know that events A and B are mutually exclusive, do you have enough information to compute P(A or B)? Explain.
Critical Thinking You are given the information that P A 5 0.30 and P B 5 0.40.(a) Do you have enough information to compute P(A and B)? Explain.(b) If you know that events A and B are independent, do you have enough information to compute P(A and B)? Explain.
Critical Thinking For a class activity, your group has been assigned the task of generating a quiz question that requires use of the formula for conditional probability to compute P B | A . Your group comes up with the following question: “If P A and B 5 0.40 and P A 5 0.20, what is the value of
Salary Raise: Men According to the same survey quoted in Problem 9, of the men interviewed, 20% had asked for a raise and 59% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, fi nd the following probabilities: P(man asked for
Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable.Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure.A random sample of 1000 people with known allergies to poison ivy
Basic Computation Compute: (a) P7,2 (b) C7,2 (c) P3,3 (d) C4,4
Statistical Literacy Which of the following are continuous variables, and which are discrete?(a) Number of traffi c fatalities per year in the state of Florida(b) Distance a golf ball travels after being hit with a driver(c) Time required to drive from home to college on any given day(d) Number of
Statistical Literacy Which of the following are continuous variables, and which are discrete?(a) Speed of an airplane(b) Age of a college professor chosen at random(c) Number of books in the college bookstore(d) Weight of a football player chosen at random(e) Number of lightning strikes in Rocky
Statistical Literacy Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.(a) x 0 1 2 P(x) 0.25 0.60 0.15(b) x 0 1 2 P(x) 0.25 0.60 0.20
Statistical Literacy At State College all classes start on the hour, with the earliest start time at 7 a.m. and the latest at 8 p.m. A random sample of freshmen showed the percentages preferring the listed start times.Start Time 7 or 8 A.M. 9,10,or 11A.M. 12 or 1 P.M. 1 P.M., or later after 5
Statistical Literacy Consider two discrete probability distributions with the same sample space and the same expected value. Are the standard deviations of the two distributions necessarily equal? Explain.
Statistical Literacy Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? Explain or give an example.
Basic Computation: Expected Value and Standard Deviation Consider the probability distribution shown in Problem 3(a). Compute the expected value and the standard deviation of the distribution.
Basic Computation: Expected Value For a fundraiser, 1000 raffl e tickets are sold, and the winner is chosen at random. There is only one prize, $500 in cash. You buy one ticket.(a) What is the probability you will win the prize of $500?(b) Your expected earnings can be found by multiplying the
Marketing: Income What is the income distribution of super shoppers (see Problem 10). In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.Income range 5–15
Criminal Justice: Parole USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining fi ve prisoners up for parole.Let x 5 number of prisoners out of fi ve on parole who become repeat
Expected Value: Life Insurance Jim is a 60-year-old male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefi t) life insurance policy until he is 65.The policy will expire on his 65th birthday. The probability of death in a given year is provided by the
Expected Value: Life Insurance Sara is a 60-year-old female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefi t) life insurance policy until she is 65.The policy will expire on her 65th birthday. The probability of death in a given year is provided by
Expand Your Knowledge: Linear Functions and Combinations of Independent Random Variables: Golf How can we compute the mean and standard deviation of new random variables created by a linear function of one random variable or a linear combination of two independent random variables? The following
Expand Your Knowledge: Linear Functions and Combinations of Independent Random Variables: Repair Service A computer repair shop has two work centers. The fi rst center examines the computer to see what is wrong, and the second center repairs the computer. Let x1 and x2 be random variables
Expand Your Knowledge: Linear Functions and Combinations of Independent Random Variables: Insurance Risk Insurance companies know the risk of insurance is greatly reduced if the company insures not just one person, but many people. How does this work? Let x be a random variable representing the
Statistical Literacy What does the random variable for a binomial experiment of n trials measure?
Statistical Literacy What does it mean to say that the trials of an experiment are independent?
Statistical Literacy For a binomial experiment, how many outcomes are possible for each trial? What are the possible outcomes?
Statistical Literacy In a binomial experiment, is it possible for the probability of success to change from one trial to the next? Explain.
Interpretation Suppose you are a hospital manager and have been told that there is no need to worry that respirator monitoring equipment might fail because the probability any one monitor will fail is only 0.01. The hospital has 20 such monitors and they work independently. Should you be more
Interpretation From long experience a landlord knows that the probability an apartment in a complex will not be rented is 0.10. There are 20 apartments in the complex, and the rental status of each apartment is independent of the status of the others. When a minimum of 16 apartment units are
Critical Thinking In an experiment, there are n independent trials. For each trial, there are three outcomes, A, B, and C. For each trial, the probability of outcome A is 0.40; the probability of outcome B is 0.50; and the probability of outcome C is 0.10. Suppose there are 10 trials.(a) Can we use
Critical Thinking In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the
Critical Thinking: Simulation Central Eye Clinic advertises that 90% of its patients approved for LASIK surgery to correct vision problems have successful surgeries.(a) In the random-number table, assign the digits 0 through 8 to the event“successful surgery” and the digit 9 to the event
Basic Computation: Binomial Distribution Consider a binomial experiment with n 5 7 trials where the probability of success on a single trial is p 5 0.30.(a) Find P1r 5 02.(b) Find P1r 12 by using the complement rule.
Basic Computation: Binomial Distribution Consider a binomial experiment with n 5 7 trials where the probability of success on a single trial is p 5 0.60.(a) Find P1r 5 72.(b) Find P1r 62 by using the complement rule.
Basic Computation: Binomial Distribution Consider a binomial experiment with n 5 6 trials where the probability of success on a single trial is p 5 0.85.(a) Find P1r 12.(b) Interpretation If you conducted the experiment and got fewer than 2 successes, would you be surprised? Why?
Basic Computation: Binomial Distribution Consider a binomial experiment with n 5 6 trials where the probability of success on a single trial is p 5 0.20.(a) Find P10 r 22.(b) Interpretation If you conducted the experiment and got 1 or 2 successes, would you be surprised? Why?
Binomial Probabilities: Coin Flip A fair quarter is fl ipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in Table 2 of the Appendix and compare the table
Binomial Probabilities: Multiple-Choice Quiz Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has fi ve answers, of which only one is correct. Since Richard has not attended class recently, he doesn’t know any of the answers. Assuming that Richard
Ecology: Wolves The following is based on information taken from The Wolf in the Southwest: The Making of an Endangered Species, edited by David Brown (University of Arizona Press). Before 1918, approximately 55% of the wolves in the New Mexico and Arizona region were male, and 45% were female.
Sociology: Ethics The one-time fl ing! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fl ing. About 10% of all adults deliberately do a one-time fl ing and feel no guilt about it
Sociology: Mother-in-Law Sociologists say that 90% of married women claim that their husband’s mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). (See the source in Problem 18.) Suppose that six married women are having coffee together
Sociology: Dress Habits A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood fl ow to the brain, diminishing cerebral functions (Source: Chances: Risk and Odds in Everyday Life,
Psychology: Myers–Briggs Approximately 75% of all marketing personnel are extroverts, whereas about 60% of all computer programmers are introverts(Source: A Guide to the Development and Use of the Myers–Briggs Type Indicator, by Myers and McCaulley).(a) At a meeting of 15 marketing personnel,
Business Ethics: Privacy Are your fi nances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA

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