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introduction to probability statistics

Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions

4.53 Grant Funding Whether a grant proposal is funded quite often depends on the reviewers. Suppose a group of research proposals was evaluated by a group of experts as to whether the proposals were worthy of funding. When these same proposals were submitted to a second independent group of
4.52 Drug Testing Some companies are testing prospective employees for drug use, with the intent of improving efficiency and reducing absenteeism, acci- dents, and theft. Opponents claim that this procedure is creating a class of unhirables and that some persons may be placed in this class because
4.51 Refer to Exercise 4.50.a. Are events A and B mutually exclusive? Explain.b. Are events A and B independent? Explain.
4.50 An experiment can result in one or both of events A and B with the probabilities shown in this probability table:Find the following probabilities:a. P(A)d. P(AUB)b. P(B)c. P(ANB)e. P(A|B)f. P(BA) A A B 0.34 0.46 Be 0.15 0.05
4.49 Suppose that P(A)= 0.4 and P(AB)=0.12.a. Find P(BA).b. Are events A and B mutually exclusive?c. If P(B) = 0.3, are events A and B independent?
4.48 Suppose that P(A) = 0.3 and P(B) = 0.5. If events A and B are mutually exclusive, find these probabilities:a. P(ANB)b. P(AUB)
4.47 Suppose that P(A) = 0.4 and P(B) = 0.2. If events A and B are independent, find these probabilities:a. P(AB)b. P(AUB)
4.46 Refer to Exercise 4.45.a. Are events A and B independent? Mutually exclusive?b. Are events A and C independent? Mutually exclusive?
4.45 Dice An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, and C are defined as follows: A: Observe a number less than 4 B: Observe a number less than or equal to 2 C: Observe a number greater than 3 Find the probabilities
4.44 Refer to Exercise 4.40.a. Are events A and B independent?b. Are events A and B mutually exclusive?
4.43 Refer to Exercise 4.40. Use the Addition and Multiplication Rules to find these probabilities:a. P(AUB)b. P(AB)c. P(BNC) Do the results agree with those obtained in Exercise 4.40?
4.42 Refer to Exercise 4.40. Use the definition of conditional probability to find these probabilities:b. P(B|C)a. P(A|B) Do the results agree with those obtained in Exercise 4.40?
4.41 Refer to Exercise 4.40. Use the definition of a complementary event to find these probabilities:a. P(A)b. P((AB)) Do the results agree with those obtained in Exercise 4.40?
4.40 An experiment can result in one of five equally likely simple events, E1, E2,..., Es. Events A, B, and Care defined as follows: A: E, E3 P(A)=0.4 B: E1, E2, E4, Es P(B)=0.8 C: E3, EA P(C)=0.4 Find the probabilities associated with these compound events by listing the simple events in each.a.
Two cards are drawn from a deck of 52 cards. Calculate the probability that the draw includes an ace and a 10.
Refer to the probability table in Example 4.18, which is reproduced below.Are events D and A independent? Explain. Too High Right Amount Too Little (A) (B) (C) Child in university (D) 0.35 0.08 0.01 No child in university (E) 0.25 0.20 0.11
Toss two coins and observe the outcome. Define these events: A: Head on the first coin B: Tail on the second coin Are events A and B independent?
Coin Tosses at Football Games A football team is involved in two overtime periods during a given game, so that there are three coin tosses. If the coin is fair, what is the probability that they lose all three tosses?
In a colour preference experiment, eight toys are placed in a container. The toys are identical except for colour two are red, and six are green. A child is asked to choose two toys at random. What is the probability that the child chooses the two red toys?
Suppose a group of 40 first-year science students at Brock University were classified according to their gender and drinking habits, as shown in Table 4.6. One student is selected at random from that group of 40 people.1. What is the probability the student drinks? 2. What is the probability the
In a telephone survey of 1000 adults, respondents were asked about the expense of a university education and the relative necessity of some form of financial assistance. The respondents were classified according to whether they currently had a child in university and whether they thought the loan
An oil-prospecting firm plans to drill two exploratory wells. Past evidence is used to assess the possible outcomes listed in Table 4.4. Outcomes for Oil-Drilling Experiment Event Description Neither well produces oil or gas Probability 0.80 Exactly one well produces oil or gas 0.18 C Both wells
Two fair coins are tossed, and the outcome is recorded. These are the events of interest: A: Observe at least one head B: Observe at least one tail Define the events A, B, AB, AUB, and A as collections of simple events, and find their probabilities.
4.39 Monkey Business A monkey is given 12 blocks: 3 shaped like squares, 3 like rectangles, 3 like triangles, and 3 like circles. If it draws three of each kind in order-say, 3 triangles, then 3 squares, and so on would you suspect that the monkey associates identically shaped figures? Calculate
4.38 Cramming A student prepares for an exam by studying a list of 10 problems. She can solve 6 of them. For the exam, the instructor selects 5 questions at random from the list of 10. What is the probability that the student can solve all 5 problems on the exam?
4.37 Gender Bias? Consider the following case. The eight-member Human Relations Advisory Board considered the complaint of a woman who claimed discrimination, based on her gender, on the part of a local surveying company. The board, composed of five women and three men, voted 5-3 in favour of the
4.36 100-Metre Run, again Refer to Exercise 4.14, in which a 100-metre sprint is run by John, Bill, Ed, and Dave. Assume that all the runners are equally qualified, so that any order of finish is equally likely. Use the mn Rule or permutations to answer these questions:a. How many orders of finish
4.35 The NHL Professional ice hockey is very popular in Canada. National Hockey League (NHL) teams are divided into six divisions. Some information is shown in the table.Two teams, one from each group, are randomly selected to play an exhibition game.a. How many pairs of teams can be chosen?b. What
4.34 Traffic Problems Two city council members are to be selected from a total of five to form a sub- committee to study the city's traffic problems.a. How many different subcommittees are possible?b. If all possible council members have an equal chance of being selected, what is the probability
4.33 A Hospital Survey A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. If a sample of 10 nurses is to be selected from a total of 90, how many different samples can be selected? (HINT: Is order important in determining the
4.32 Poker, Again Refer to Exercise 4.31. You have a poker hand containing four of a kind.a. How many possible poker hands can be dealt?b. In how many ways can you receive four cards of the same face value and one card from the other 48 available cards?c. What is the probability of being dealt four
4.31 Playing Poker Five cards are selected from a 52-card deck for a poker hand.a. How many simple events are in the sample space?b. A royal flush is a hand that contains the A, K, Q. J, and 10, all in the same suit. How many ways are there to get a royal flush?c. What is the probability of being
4.30 Dinner at a French Restaurant A French restaurant in Winnipeg, Manitoba, offers a special summer menu in which, for a fixed dinner cost, you can choose from one of two salads, one of two entrees, and one of two desserts. How many different dinners are available?
4.29 A Card Game Three students are playing a card game. They decide to choose the first person to play by each selecting a card from the 52-card deck and looking for the highest card in value and suit. They rank the suits from lowest to highest: clubs, diamonds, hearts, and spades.a. If the card
4.28 Vacation Plans Your family vacation involves an air flight, a rental car, and a hotel stay in Halifax. If you can choose from three air carriers, five car rental agencies, and four major hotel chains, how many options are available for your vacation accommoda- tions?
4.27 Itineraries A businessman in Montreal is preparing an itinerary for a visit to six major cities. The distance travelled, and hence the cost of the trip, will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible?
4.26 What to Wear? You own 4 pairs of jeans, 12 clean T-shirts, and 4 wearable pairs of sneakers. How many outfits (jeans, T-shirt, and sneakers) can you create?
4.24 Coins Four coins are tossed. How many simple events are in the sample space?
4.23 Dice Three dice are tossed. How many simple events are in the sample space?
4.22 Choosing People, again In how many ways can you select two people from a group of 20 if the order of selection is not important?
4.21 Choosing People In how many ways can you select five people from a group of eight if the order of selection is important?
4.20 Combinations Evaluate these combinations:a. Cb. Coc. Cd. C
4.19 Permutations Evaluate the following permu- tations. (HINT: Your scientific calculator may have a function that allows you to calculate permutations and combinations quite easily.)a. Pb. Poc. Pod. P20
Five manufacturers produce a certain electronic device, whose quality varies from manufacturer to manufacturer. If you were to select three manufacturers at random, what is the chance that the selection would contain exactly two of the best three?
A piece of equipment is composed of five parts that can be assembled in any order. A test is to be conducted to determine the time necessary for each order of assembly. If each order is to be tested once, how many tests must be conducted?
Three lottery tickets are drawn from a total of 50. If the tickets will be distributed to each of three employees in the order in which they are drawn, the order will be impor- tant. How many simple events are associated with the experiment?
A truck driver can take three routes from city A to city B, four from city B to city C, and three from city C to city D. If, when travelling from A to D, the driver must drive from A to B to C to D, how many possible A-to-D routes are available?
How many simple events are in the sample space when three coins are tossed?
A candy dish contains one yellow and two red candies. Two candies are selected one at a time from the dish, and their colours are recorded. How many simple events are in the sample space S?
Two dice are tossed. How many simple events are in the sample space S?
4.16 Health Care Most Canadians feel that health care is the most important issue. Research Canada: An Alliance for Health Discovery (www.rc-rc.ca) released the result of its first public opinion survey on health research in Canada. The results are shown in the table.Suppose that one person is
4.15 Fruit Flies In a genetics experiment, the researcher mated two Drosophila fruit flies and observed the traits of 300 offspring. The results are shown in the table.One of these offspring is randomly selected and observed for the two genetic traits.a. What is the probability that the fly has
4.14 100-Metre Run Four equally qualified runners, John, Bill, Ed, and Dave, run a 100-metre sprint, and the order of finish is recorded.a. How many simple events are in the sample space?b. If the runners are equally qualified, what probability should you assign to each simple event?c. What is the
4.13 Tea Tasters A food company plans to con- duct an experiment to compare its brand of tea with that of two competitors. A single person is hired to taste and rank each of three brands of tea, which are unmarked except for identifying symbols A, B, and C.a. Define the experiment.b. List the
4.12 Jury Duty, again Refer to Exercise 4.11. Sup- pose that there are six prospective jurors, four men and two women, who might be impanelled to sit on the jury in a criminal case. Two jurors are randomly selected from these six to fill the two remaining jury seats.a. List the simple events in the
4.11 Jury Duty Three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.a. Define the experiment.b. List the simple events in S.c. If each person is just as likely to be a man as a woman, what
4.10 Roulette The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are num- bered 1, 2,..., 36, and the remaining two are marked 0 and 00. The wheel is spun, and a pocket is identified as the "winner." Assume that the observance of any one pocket is just as likely as any
4.9 Need Eyeglasses? A survey classified a large number of adults according to whether they were judged to need eyeglasses to correct their reading vision and whether they used eyeglasses when reading.The proportions falling into the four categories are shown in the table. (Note that a small
4.8 The Urn Problem, continued Refer to Exer- cise 4.7. A ball is randomly selected from the urn containing three red and two yellow balls. Its colour is noted, and the ball is returned to the urn before a second ball is selected. List the additional five simple events that must be added to the
4.7 The Urn Problem An urn contains three red and two yellow balls. Two balls are randomly selected and their colours recorded. Use a tree diagram to list the 20 simple events in the experiment, keeping in mind the order in which the balls are drawn.
4.6 Preschool or Not? On the first day of kin- dergarten, the teacher randomly selects 1 of his 25 students and records the student's gender, as well as whether or not that student had gone to preschool.a. How would you describe the experiment?b. Construct a tree diagram for this experiment. How
4.5 Four Coins A jar contains four coins: a nickel, a dime, a quarter, and a loonie. Three coins are randomly selected from the jar.a. List the simple events in S.b. What is the probability that the selection will con- tain the loonie?c. What is the probability that the total amount drawn will
4.4 Free Throws A particular basketball player hits 70% of her free throws. When she tosses a pair of free throws, the four possible simple events and three of their associated probabilities are as given in the table:a. Find the probability that the player will hit on the first throw and miss on
4.3 A sample space contains 10 simple events: E1, E2E10. If P(E)=3P(E2)=0.45 and the remaining simple events are equiprobable, find the probabilities of these remaining simple events.
4.2 A sample space S consists of five simple events with these probabilities:a. Find the probabilities for simple events E4 and Es.b. Find the probabilities for these two events: A=(E, E3, E4) B={E2, E3)c. List the simple events that are either in event A or event B or both.d. List the simple
4.1 Tossing a Die An experiment involves tossing a single die. These are some events: A: Observe a 2 B: Observe an even number C: Observe a number greater than 2 D: Observe both A and B E: Observe A or B or both F: Observe both A and Ca. List the simple events in the sample space.b. List the simple
A candy dish contains one yellow and two red candies. You close your eyes, choose two candies one at a time from the dish, and record their colours. What is the probabil- ity that both candies are red?
Canada is the world's second largest country by total area. Canadians adhere to a wide variety of religions. Statistics Canada (2001 census) reports that 77.1% of Canadians were identified as being Christians, about 16.5% of Canadians declared no religious affiliation, and the remaining 6.4% were
A medical technician records a person's blood type and Rh factor. List the simple events in the experiment.
Experiment: Record a person's blood type. The four mutually exclusive possible out- comes are these simple events: E: Blood type A E2: Blood type B E3: Blood type AB E4: Blood type O The sample space is S={E1, E2, E3, E4], or S = {A, B, AB, O].
Experiment: Toss a single coin and observe the result. These are the simple events: E: Observe a head (H) E2: Observe a tail (T) The sample space is S= {E, E2} or more simply, S = {H, T}.
We can define the events A and B for the die-tossing experiment: A: Observe an odd number B: Observe a number less than 4 Since event A occurs if the upper face is 1, 3, or 5, it is a collection of three sim- ple events, and we write A = {E, E3, Es). Similarly, the event B occurs if the upper face
Experiment: Toss a die and observe the number that appears on the upper face. List the simple events in the experiment.
How to Calculate the Probability of an Event The Difference between Mutually Exclusive and Independent Events
Project 3-B: Child Safety Seat Survey, continued Based on the same survey, the following table refers to the weight (in kg), height (in cm), and gender of a random sample of 40 children chosen from the large data set.a. Draw a scatterplot of weights of female children with their respective heights.
Canada has a Road Safety Vision of having the safest roads in the world. Yet, the lead- ing cause of death of Canadian children remains vehicle crashes. In 2006, a national child safety seat survey was conducted by an AUTO21 research team in collaboration with Transport Canada to empirically
3. Answer the questions: Does the price of an athletic team, specifically in the NHL, convey something about its quality? Which variables did you use in arriving at your answer?Are higher-paid hockey players actually better than lower-salaried ones? Despite the league's new salary cap, the 30 teams
2. Look at the variables in pairs. Which pairs of variables are positively correlated? Which are negatively correlated? Do any pairs exhibit little or no correlation? Are some of these results counterintuitive? Can you offer an explanation for these cases?Are higher-paid hockey players actually
1. Look at each variable individually. What can you say about symmetry? About outliers?Are higher-paid hockey players actually better than lower-salaried ones? Despite the league's new salary cap, the 30 teams in the NHL in the 2005-2006 season had widely different payrolls, starting with the New
3.39 Smartphones The table below shows the EX0339 prices of nine U.S. Verizon smartphones along with their overall score (on a scale of 0-100) in a con- sumer rating survey presented by Consumer Reports.a. Plot the nine data points using a scatterplot. Describe the form, direction, and strength of
3.38 Happy in the Air? continued The following table reveals complaints against Air Canada and major U.S. airlines in a given year."a. Construct a scatterplot for the data.b. Describe the form, direction, and strength of the pat- tern in the scatterplot.c. Are there any outliers in the scatterplot?
3.36 Test-Interviews Of two personnel evaluation techniques available, the first requires a two-hour test-interview while the second can be completed in less than an hour. The scores for each of the eight individuals who took both tests are given in the next table.a. Construct a scatterplot for the
3.35 Travellers to Canada The number of nights x (in thousands) and the spending in Canada y (in millions of dollars) for the top 15 coun- tries of origin in 2005 are given in the table.a. Construct a scatterplot for the data (x and y).b. Describe the form, direction, and strength of the pat- tern
3.34 Armspan and Height Leonardo DaVinci (1452-1519) drew a sketch of a man, indicating that a persons armspan (measuring across the back with arms outstretched to make a "T") is roughly equal to the person's height. To test this claim, we measured eight people with the following results:a. Draw a
3.33 The Religious Cleavage in Canada Mendelsohn and Nadea (1997), in Canadian Journal of Political Science, reported the strength of the religious cleavage in Canada (outside Quebec). The results are shown below.a. What variables have been measured in this survey? Are they qualitative or
3.32 Internet Access from Home The table EX0332 below (see Exercise 1.50) shows DSL versus cable users per 100 members of the population.a. What variables have been measured in this experiment? Are they qualitative or quantitative?b. Use one of the graphical methods given in this chapter to
3.31 Pottery, continued Here is the per- centage of aluminum oxide, the percentage of iron oxide, and the percentage of magnesium oxide in five samples collected at Ashley Rails in the United Kingdom.a. Find the correlation coefficients describing the relationships between aluminum and iron oxide
3.30 Pottery, continued In Exercise 1.56, we analyzed the percentage of aluminum oxide in 26 samples of Romano-British pottery found at four different kiln sites in the United Kingdom. 14 Since one of the sites provided only two measurements, that site is eliminated, and comparative box plots of
3.29 Aaron Rodgers The number of passes completed and the total number of passing yards were recorded for Aaron Rodgers for each of the 15 regular season games that he played in the fall of 2010:a. Draw a scatterplot to describe the relationship between number of completions and total passing yards
3.28 Federal Contaminated Sites (2005) The data in the following table give the number of federal contaminated sites for provinces and territories along with the size of the province/territory, and the percentage of the total area.a. Draw a scatterplot with MINITAB. Is there any clear pattern in
3.27 Movie Money, continued The data from Exercise 3.26 were entered into a MINITAB worksheet, and the following output was obtained.a. Use the MINITAB output or the original data to find the correlation between first weekend and total gross.b. Which of the two variables would you clas- sify as the
3.26 Movie Money Does the opening weekend adequately predict the success or failure of a new movie? In 2001, 36 movies were investigated in Entertainment Weekly, and the following variables were recorded. "I The movie's first weekend's gross earnings (in millions of dollars) The movie's total gross
3.25 Peak Current Using a chemical proce- dure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given amount of nickel (in parts per billion) is added to a buffer. The data are shown here:Use a graph to describe the
3.24 Cheese, again! The demand for healthy foods that are low in fats and calories has resulted in a large number of "low-fat" and "fat-free" products at the supermarket. The table shows the numbers of calories and the amounts of sodium (in milligrams) per slice for five different brands of
3.23 Import Sale and Domestic Production in Japan The Japan Automobile Manufacturers Association of Canada, in their Annual Review 2006, provided the following two bar charts regarding import sales of automobiles and domestic automobile produc- tion in Japan, respectively.a. What variables have
3.22 Cheese, Please! Health-conscious con- sumers often consult the nutritional information on food packages in an attempt to avoid foods with large amounts of fat, sodium, or cholesterol. The fol- lowing information was taken from eight different brands of cheese slices:a. Which pairs of variables
3.21 Professor Asimov Professor Isaac Asimov was one of the most prolific writers of all time. He wrote nearly 500 books during a 40-year career prior to his death in 1992. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given
Scatterplots, Correlation, and the Regression Line The data from Example 2.16 give the front and rear leg rooms (in centimetres) for nine different sport-utility ve- hicles, as shown in Table 3.9:1. If you did not save the MINITAB worksheet from Chapter 2, enter the data into the first three
Comparative Line and Bar Charts Suppose that the 105 students whose status was tabulated in Example 1.17 were from the University of Windsor (UW), and that an- other 100 students from an introductory statistics class at the University of New Bruns- wick (UNB) were also interviewed. Table 3.8 shows
Scatterplots, Correlation, and the Regression Line The data from Example 2.15 give the front and rear leg rooms (in centimetres) for nine different sport utility vehicles, as shown in Table 3.7:8Scatterplots, Correlation, and the Regression Line The data from Example 2.15 give the front and rear

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