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Understanding Basic Statistics 6th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

The following data are based on information from the book The Rating Guide to Life in America€™s Small Cities (by G. S. Thomas, Prometheus Books). Let x be the percentage of 16- to 19-year-olds not in school and not high-school graduates. Let y be the reported violent crimes per 1000
The following data are based on information from the Harvard Business Review (Vol. 72, No. 1). Let x be the number of different research programs and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs
Data for this problem are based on information taken from Prehistoric New Mexico: Background for Survey (by D. E. Stuart and R. P. Gauthier, University of New Mexico Press). It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher
Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at
Consider the data from Problem 9. (a) Make a residual plot for the least-squares model. (b) Use the residual plot to comment about the appropriateness of the least-squares model for these data. (See Problem 19.)
(a) Suppose you are given the following (x, y) data pairs:Show that the least-squares equation for these data is Å· = 0.143 + 1.071x (rounded to three digits after the decimal). (b) Now suppose you are given these (x, y) data pairs: Show that the least-squares equation for these data
We use the form ŷ = α + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant α is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes α is referred to as the
Refer to the description of a computer display for regression in Problem 5. The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/24 hr). The data are based on information from
An economist is studying the job market in Denver-area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (in hundreds of
You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). The
Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No. 4):Complete parts (a) through (e), given
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following informationComplete parts (a) through (c),
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner (University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality
A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information:Complete parts (a) through (c), given
Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year-old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females:Complete
Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients€™ homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she has kept careful
Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of garden seeds. At the Healthy Crunch home office, they use the weight of incoming mail to determine how many of their employees are to be assigned to collecting coupons and mailing out seed packages on a
Consider the experiment of tossing a fair coin 3 times. For each coin, the possible outcomes are heads or tails. (a) List the equally likely events of the sample space for the three tosses. (b) What is the probability that all three coins come up heads? Notice that the complement of the event “3
(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.
Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.Similarities and Differences in a
(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 in part (a). Do the probabilities add up to 1? Should they add up to 1? Explain. (c)
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:Time of Day When Best Ideas Occur(a) Assuming that the time interval includes the left limit and all the times up to but not including the right
A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds
Sometimes probability statements are expressed in terms of odds.The odds in favor of an event A are the ratioFor instance, if P(A) = 0.60, then P(Ac) = 0.40 and the odds in favor of A are 0.60/0.40 = 6/4 = 3/2 , written as 3 to 2 or 3:2. (a) Show that if we are given the odds in favor of event A as
Betting odds are usually stated against the event happening (against winning).The odds against event W are the ratioIn horse racing, the betting odds are based on the probability that the horse does not win. (a) Show that if we are given the odds against an event W as a:b, the probability of not W
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 probability that a
What is the law of large numbers? If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.
An investment opportunity boasts that the chance of doubling your money in 3 years is 95%. However, when you research the details of the investment, you estimate that there is a 3% chance that you could lose the entire investment. Based on this information, are you certain to make money on this
Consider a family with 3 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events “boy” and “girl” are independent. (a) List the equally likely events for the genders of the 3 children, from oldest to
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 part
Consider the following events for a driver selected at random from the general population: A = driver is under 25 years old B = driver has received a speeding ticket Translate each of the following phrases into symbols. (a) The probability the driver has received a speeding ticket and is under 25
Consider the following events for a college student selected at random: A = student is female B = 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 student is
M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs (link to the Mars company website from the Brase/Brase statistics site at www.cengagebrain.com), the distribution of colors for plain M&M candies isSuppose you have a large bag of plain M&M candies
Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening of at least 3 feet. The
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)).
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)).
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?
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?
You draw two cards from a standard deck of 52 cards without replacing the first 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 probability of drawing an Ace
You draw two cards from a standard deck of 52 cards without replacing the first 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 drawing a 10 and a 3
You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle 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 on 2nd). (d) Find the
You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle 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 2nd). (d) Find the
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 3 and 9 years
Based on data from the Statistical Abstract of the United States, 112th edition, only about 14% of senior citizens (65 years old or older) get the flu each year. However, about 24% of the people under 65 years old get the flu each year. In the general population, there are 12.5% senior citizens (65
In this problem, you are asked to solve part of the Focus Problem at the beginning of this chapter. In his book Chances: Risk and Odds in Everyday Life, James Burke says that there is a 72% chance a polygraph test (lie-detector test) will catch a person who is in fact lying. Furthermore, there is
Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (ˆ’) indicates that the patient does not
In an article entitled €œDiagnostic Accuracy of Fever as a Measure of Postoperative Pulmonary Complications€ (Heart and Lung, Vol. 10, No. 1, p. 61), J. Roberts and colleagues discuss using a fever of 38oC or higher as a diagnostic indicator of postoperative atelectasis
Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United States, published by the Food Marketing Institute, Washington, D.C. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent
In a sales-effectiveness seminar, a group of sales representatives tried two approaches to selling a customer a new automobile: the aggressive approach and the passive approach. For 1160 customers, the following record was kept:Suppose a customer is selected at random from the 1160 participating
Given P(A) = 0.3 and P(B) = 0.4: (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.1, compute P(A or B).
Given P(A) = 0.7 and P(B) = 0.4: (a) Can events A and B be mutually exclusive? Explain. (b) If P(A and B) = 0.2, compute P(A or B).
Given P(A) = 0.2 and P(B) = 0.4: (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A and B).
Given P(A) = 0.7 and P(B) = 0.8: (a) If A and B are independent events, compute P(A and B). (b) If P(B | A) = 0.3, compute P(A and B).
Given (1A) = 0.2, P(B) = 0.5, and P(A | B) = 0.3: (a) Compute P(A and B). (b) Compute P(A or B).
Given P(Ac) = 0.8, P(B) = 0.3, and P(B | A) = 0.2: (a) Compute P(A and B). (b) Compute P(A or B).
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 P(A |
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?
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 Extension: What is the
Compute P5,2.
Compute P8,3.
Compute P7,7.
Compute P9,9.
Compute C5,2.
Compute C8,3.
Compute C7,7.
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?
Compute C8,8.
There are three nursing positions to be filled 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 qualified for all three of the positions. Determine the number of
In the Cash Now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is $1 million, the second prize is $100,000, and the third prize is $10,000. Determine the total number of different ways in which
The University of Montana ski team has five entrants in a men’s downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the five team entrants achieve first, second, and third places?
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?
There are 15 qualified applicants for 5 trainee positions in a fast-food management program. How many different groups of trainees can be selected?
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 he did
The qualified applicant pool for six management trainee positions consists of seven women and five 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 If the
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 can be selected
(a) Draw a tree diagram to display all the possible heads–tails sequences that can occur when you flip 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 exactly
(a) Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a die. (b) How many outcomes contain a heads and a number greater than 4? (c) Probability Extension Assuming the outcomes displayed in the tree diagram are all equally likely, what is the
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 all possible
(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 probability that
Consider the following two events for an individual: A = owns a cell phone B = owns a laptop computer Translate each event into words. (a) Ac (b) A and B (c) A or B (d) A | B (e) B | A
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, find the following probabilities: P(man asked for a raise); P(man
Drop a thumbtack and observe how it lands. (a) Describe how you could use a relative frequency to estimate the probability that a thumbtack will land with its fl at side down. (b) What is the sample space of outcomes for the thumbtack? (c) How would you make a probability assignment to this sample
Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at the 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 participated in the
In a game of craps, you roll two fair dice. Whether you win or lose depends on the sum of the numbers appearing on the tops of the dice. Let x be the random variable that represents the sum of the numbers on the tops of the dice.(a) What values can x take on?(b) What is the probability distribution
Class records at Rockwood College indicate that a student selected at random has probability 0.77 of passing French 101. For the student who passes French 101, the probability is 0.90 that he or she will pass French 102. What is the probability that a student selected at random will pass both
There is money to send two of eight city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of two council members can be selected from the eight who want to go to the
Compute: (a) P7,2 (b) C7,2 (c) P3,3 (d) C4,4
There are five multiple-choice questions on an exam, each with four possible answers. Determine the number of possible answer sequences for the five questions. Only one of the sets can contain all five correct answers. If you are guessing, so that you are as likely to choose one sequence of answers
A student must satisfy the literature, social science, and philosophy requirements this semester. There are four literature courses to select from, three social science courses, and two philosophy courses. Make a tree diagram showing all the possible sequences of literature, social science, and
You have a combination lock. Again, to open it you turn the dial to the right and stop at a first number; then you turn it to the left and stop at a second number. Finally, you turn the dial to the right and stop at a third number. Suppose you remember that the three numbers for your lock are 2, 9,
You are considering 2 facial cosmetic surgeries. These are elective surgeries and their outcomes are independent. The probability of success for each surgery is 0.90. What is the probability of success for both surgeries? If the probability of success for both surgeries is less than 0.85, you will
You are applying for two jobs, and you estimate the probability of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are independent. (a) Compute the probability of getting offers for both jobs. How does this
You are given the information that P(A) = 0.30 and P(B) = 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.
You are given the information that P(A) = 0.30 and P(B) = 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.
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) = 0.40 and P(A) = 0.20, what is the value of P(B | A)?”
Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one (USA Today). According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked for a raise, 45%
Which of the following are continuous variables, and which are discrete? (a) Number of traffic 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 ships in Pearl
What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). In 1851 there were 25,466
The following data are based on information taken from Daily Creel Summary, published by the Paiute Indian Nation, Pyramid Lake, Nevada. Movie stars and U.S. presidents have fished Pyramid Lake. It is one of the best places in the lower 48 states to catch trophy cutthroat trout. In this table, x =
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 five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders. The methods of Section

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