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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

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
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
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
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
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
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
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
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,
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
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)
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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.
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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,
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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,
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
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
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
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
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

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