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elementary statistics

Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions

[EX04-136] The Federal Highway Administration periodically tracks the number of licensed vehicle drivers by gender and by age. The following table shows the results of the administration’s findings in 2002.Age Group (years) Male Female 19 and under 4,772,152 4,526,106 20–24 8,424,540 8,115,247
One thousand persons screened for a certain disease are given a clinical exam. As a result of the exam, the sample of 1000 persons is classified according to height and disease status.Disease Status Height None Mild Moderate Severe Total Tall 122 78 139 61 400 Medium 74 51 90 35 250 Short 104 71
[EX04-134] The number of people living in the 50 U.S. states and the District of Columbia in September 2004 is reported by age groups in the following table.Age Group Percentage Number (1000s)0–17 25% 73,447.7 18–24 10% 28,855.7 25–34 13% 39,892.5 35–49 23% 66,620.3 50 29% 84,119.8 Source:
The Federal Railroad Administration provided the top five categories of violations for the CSX railroad for the years 1999–2003 in the following table. There were a total of 1897 violations.The information was contained in the December 29, 2004, Democrat and Chronicle article titled “Rail cop
A company that manufactures shoes has three factories. Factory 1 produces 25% of the company’s shoes, Factory 2 produces 60%, and Factory 3 produces 15%. One percent of the shoes produced by Factory 1 are mislabeled, 0.5% of those produced by Factory 2 are mislabeled, and 2% of those produced by
One thousand employees at the Russell Microprocessor Company were polled about worker satisfaction. One employee is selected at random.Male Female Skilled Unskilled Skilled Unskilled Total Satisfied 350 150 25 100 625 Unsatisfied 150 100 75 50 375 Total 500 250 100 150 1000a. Find the probability
Two flower seeds are randomly selected from a package that contains five seeds for red flowers and three seeds for white flowers.a. What is the probability that both seeds will result in red flowers?b. What is the probability that one of each color is selected?c. What is the probability that both
P(M) 0.3, P(N) 0.4, and events M and N are mutually exclusive.a. Find P(M and N).b. Find P(M or N).c. Find P(M or N).d. Find P(M N).e. Find P(M N).f. Are events M and N independent? Explain.
P(R) 0.5, P(S) 0.3, and events R and S are independent.a. Find P(R and S).b. Find P(R or S).c. Find P(S).d. Find P(R S).e. Find P(S R).f. Are events R and S mutually exclusive? Explain.
a. Describe in your own words why two events cannot be independent if they are already known to be mutually exclusive.b. Describe in your own words why two events cannot be mutually exclusive if they are already known to be independent.
a. Describe in your own words what it means for two events to be mutually exclusive.b. Describe in your own words what it means for two events to be independent.c. Explain how mutually exclusive and independent are two very different properties.
From a survey of adults, 48% plan to buy candy this year at Easter. The types of candy they will buy are described in the following table.Chocolate Nonchocolate Jellybeans Cream-Filled Marshmallow Malted Don’t Know 30% 25% 13% 11% 8% 7% 6%Source: International Mass Retail Associationa. What
Graduation rates reached a record low in 2001. The percentage of students who graduate within 5 years was 41.9% for public and 55.1% for private colleges. One of the reasons for this might be that 42% of the students attend only part time.(ACT)a. What additional information do you need to determine
A box contains 25 parts, of which 3 are defective and 22 are nondefective. If 2 parts are selected without replacement, find the following probabilities:a. P(both are defective)b. P(exactly one is defective)c. P(neither is defective)
Consider the set of integers 1, 2, 3, 4, and 5.a. One integer is selected at random. What is the probability that it is odd?b. Two integers are selected at random (one at a time with replacement so that each of the five is available for a second selection). Find the probability that neither is odd;
The odds against throwing a pair of dice and getting a total of 5 are 8 to 1. The odds against throwing a pair of dice and getting a total of 10 are 11 to 1. What is the probability of throwing the dice twice and getting a total of 5 on the first throw and 10 on the second throw?
The owners of a two-person business make their decisions independently of each other and then compare their decisions. If they agree, the decision is made; if they do not agree, then further consideration is necessary before a decision is reached. If each has a history of making the right decision
You have applied for two scholarships: a merit scholarship (M) and an athletic scholarship(A). Assume the probability that you receive the athletic scholarship is 0.25, the probability you receive both scholarships is 0.15, and the probability you get at least one of the scholarships is 0.37. Use a
The July 8, 2002, issue of Democrat & Chronicle gave the results from the 2000 census that 42%of grandparents are responsible for “most of the basic needs” of a grandchild in the home. If three American grandparents are contacted, what is the probability that all three are the primary caregiver
A USA Today article titled “Survey: Records tainted—Fans want drug tests for baseball players”(June 12, 2002) quotes a USA Today/CNN Gallup Poll as finding 86% of baseball fans saying they favor testing ballplayers for steroids and other performance-enhancing drugs. If five baseball fans are
Of households in the United States, 18 million, or 17%, have three or more vehicles, as stated in USA Today (June 12, 2002), quoting the Census Bureau as the source.a. If two U.S. households are randomly selected, find the probability that both will have three or more vehicles.b. If two U.S.
The U.S. space program has a history made up of many successes and some failures. Space flight reliability is of the utmost importance in the launching of space shuttles. The reliability of the complete mission is based on all of its components.Each of the six joints in the Challenger space
Excluding job benefit coverage, approximately 49% of adults have purchased life insurance.The likelihood that those aged 18 to 24 without life insurance will purchase life insurance in the next year is 15%, and for those aged 25 to 34, it is 26%. (Opinion Research)a. Find the probability that a
A box contains four red and three blue poker chips. Three poker chips are to be randomly selected, one at a time.a. What is the probability that all three chips will be red if the selection is done with replacement?b. What is the probability that all three chips will be red if the selection is done
A single card is drawn from a standard deck.Let A be the event that “the card is a face card” (a jack, a queen, or a king), B is a “red card,” and C is“the card is a heart.” Determine whether the following pairs of events are independent or dependent:a. A and Bb. A and Cc. B and C
One student is selected at random from a group of 200 students known to consist of 140 fulltime(80 female and 60 male) students and 60 part-time (40 female and 20 male) students. Event A is “the student selected is full time,” and event C is “the student selected is female.”a. Are events A
Suppose that P(A) 0.3, P(B) 0.4, and P(A and B) 0.20.a. What is P(A B)?b. What is P(B A)?c. Are A and B independent?
Suppose that P(A) 0.3, P(B) 0.4, and P(A and B) 0.12.a. What is P(A B)?b. What is P(B A)?c. Are A and B independent?
If P(A) 0.3 and P(B) 0.4 and A and B are independent events, what is the probability of each of the following:a. P(A and B)b. P(B A)c. P(A B)
A and B are independent events, and P(A) 0.7 and P(B) 0.4. Find P(A and B).4.104 A and B are independent events, and P(A) 0.5 and P(B) 0.8. Find P(A and B).4.105 A and B are independent events, and P(A) 0.6 and P(A and B) 0.3. Find P(B).4.106 A and B are independent events, and P(A)
Determine whether each of the following pairs of events is independent:a. Rolling a pair of dice and observing a “2” on one of the dice and having a “total of 10”b. Drawing one card from a regular deck of playing cards and having a “red” card and having an “ace”c. Raining today and
Determine whether each of the following pairs of events is independent:a. Rolling a pair of dice and observing a “1” on the first die and a “1” on the second dieb. Drawing a “spade” from a regular deck of playing cards and then drawing another “spade”from the same deck without
He is the last guy you want to see in your rearview mirror when you are speeding down the highway, but research shows that a traffic ticket reduces a driver’s chance of being involved in a fatal accident, at least for a few weeks. By age group, 13.3% of all drivers are younger than age 25, 58.6%
Most Americans, 70% in fact, say frequent hand washing is the best way to fend off the flu.Despite that, when using public restrooms, women wash their hands only 62% of the time and men wash only 43% of the time. Of the adults using the public restroom at a large grocery chain store, 58%are women.
Injuries are unfortunately part of every sport.High school basketball is no exception, as the following table shows. The percentages listed are the percent of reported injuries that occur to high school male and female basketball players and the location on their body that was injured.Injury
Do people take indoor swimming lessons in the middle of the hot summer? They sure do at the Webster Aquatic Center. During the month of July 2004 alone, 179 people participated in various forms of lessons.Swim Categories Daytime Evenings Preschool 26 29 Levels 75 39 Adult and diving 4 6 Total 105
An aquarium at a pet store contains 40 orange swordfish (22 females and 18 males) and 28 green swordtails (12 females and 16 males). You randomly net one of the fish.a. What is the probability that it is an orange swordfish?b. What is the probability that it is a male fish?c. What is the
Two dice are rolled. Define events as follows:A—sum of 7, C—doubles, E—sum of 8.a. Which pairs of events, A and C, A and E, or C and E, are mutually exclusive? Explain.b. Find the probabilities P(A or C), P(A or E), and P(C or E).
One student is selected at random from a student body. Suppose the probability that this student is female is 0.5 and the probability that this student works part time is 0.6. Are the two events“female” and “working” mutually exclusive? Explain.
One student is selected from the student body of your college. Define the following events:M—the student selected is male, F—the student selected is female, S—the student selected is registered for statistics.a. Are events M and F mutually exclusive? Explain.b. Are events M and S mutually
If P(A) 0.4 and P(B) 0.5, and if A and B are mutually exclusive events, find P(A or B).
If P(A) 0.3 and P(B) 0.4, and if A and B are mutually exclusive events, find:a. P(A)b. P(B)c. P(A or B)d. P(A and B)
Explain why P(A occurring when B has occurred) 0 when events A and B are mutually exclusive.
Explain why P(A and B) 0 when events A and B are mutually exclusive.
Given P(A or B) 1.0, P(A and B) 0.3, and P(B) 0.4, find:a. P(B)b. P(A)c. P(A B)
Given P(A or B) 1.0, P(A and B) 0.7, and P(B) 0.4, find:a. P(B)b. P(A)c. P(A B)
Suppose that A and B are events defined on a common sample space and that the following probabilities are known: P(A) 0.5, P(A and B) 0.24, and P(A B) 0.4. Find P(A or B).
Suppose the rules for the carnival game in Example 4.13 were modified so that the marble drawn each time is returned to the box before the next drawing.a. Redraw the tree diagram drawn for Exercise 4.77, listing the probabilities for the game when played “with replacement.”b. What is the
Find the probability of winning $5 if you play the carnival game described in Example 4.13.a. Complete the branches of the tree diagram started in Figure 4.5, listing the probabilities for all possible drawings.b. What is the probability of drawing a red marble on the second drawing? What
Casey loves his mid-morning coffee and always stops by one of his favorite coffeehouses for a cup. When he gets take-out, there is a 0.6 chance that he will also have a pastry. He gets both coffee and a pastry as take-out with a probability of 0.48.What is the probability that he does take-out?
Nobody likes paying taxes, but this is not the way to get out of it! It is believed that 10% of all taxpayers intentionally claim some deductions to which they are not entitled. If 9% of all taxpayers both intentionally claim extra deductions and deny such when audited, find the probability that a
A and B are events defined on a sample space, with P(B) 0.4 and P(A and B) 0.5. Find P(A B).
A and B are events defined on a sample space, with P(A) 0.6 and P(A and B) 0.3. Find P(B A).
A and B are events defined on a sample space, with P(A B) 0.5 and P(B) 0.8. Find P(A and B).
A and B are events defined on a sample space, with P(A) 0.7 and P(B A) 0.4. Find P(A and B).
Union officials report that 60% of the workers at a large factory belong to the union, 90%make more than $12 per hour, and 40% belong to the union and make more than $12 per hour. Do you believe these percentages? Explain. Solve using formulas. Compare your solution to your answer to Exercise 4.28.
A parts store sells both new and used parts.Sixty percent of the parts in stock are used. Sixty one percent are used or defective. If 5% of the store’s parts are defective, what percentage is both used and defective? Solve using formulas. Compare your solution to your answer to Exercise 4.27.
If P(A) 0.4, P(A or B) 0.9, and P(A and B) 0.1, find P(B).
If P(A) 0.4, P(B) 0.5, and P(A or B) 0.7, find P(A and B).
If P(A) 0.5, P(B) 0.3, and P(A and B) 0.2, find P(A or B).
If P(A) 0.4, P(B) 0.5, and P(A and B) 0.1, find P(A or B).
According to the Sleep Channel (http://www.sleepchannel.net, September 2002), sleep apnea affects 12 million individuals in the United States. The sleep disorder interrupts breathing and can awaken its sufferers as often as five times an hour. Many people do not recognize the condition even though
According to the U.S. Pet Ownership & Demographic Sourcebook, from Pedigree Food for Dogs (USA Snapshot “Most give puppy love to just one,” February 22, 2005), about 66% of all American dog owners—some 60 million people—are owners of one dog. Based on this information, find the probability
a. If the probability that you pass the next exam in statistics is accurately assessed at 0.75, what is the probability that you will not pass the next statistics exam?b. The weather forecaster predicts that there is a “70 percent” chance of less than 1 inch of rain during the next 30-day
a. If the probability that event A occurs during an experiment is 0.7, what is the probability that event A does not occur during that experiment?b. If the results of a probability experiment can be any integer from 16 to 28 and the probability that the integer is less than 20 is 0.78, what is the
The five most popular colors for luxury cars manufactured during the 2003 model year in North America are reported here in percentages.Luxury Car Percentage Luxury Car Percentage 1. Med./Dk. Gray 23.30 4. White 12.6 2. Silver 18.8 5. Black 10.9 3. White Met. 17.8 Source: DuPont Herberts Automotive
The American Housing Survey reported its findings about the principal means of transportation to work by worker in Washington, DC, during the year of 2001.Means of Transportation Number (thousands)All workers 120,191 Automobile 105,586 Drives self 93,942 Carpool 11,644 2-person 9,036 3-person 1,635
In a 2000 census, The National Highway Traffic Safety Administration reported that, nationally, 2% of all traffic fatalities are bicycle deaths. The California Highway Patrol’s Statewide Integrated Traffic Records System reports that bicycle deaths account for 4% of the state’s traffic
A USA Today article titled “Yum Brands builds dynasty in China” (February 7, 2005) reports on how Yum Brands, the world’s largest restaurant company, is bringing the fast-food industry to China, India, and other big countries. Yum Brands, a spin-off from PepsiCo, has been delivering
During the month of August in 2002, the faculty and staff at Boise State University were asked to participate in a survey to identify the general level of satisfaction with the newly modified workweek in the summer. The following table lists how 620 respondents answered the question: “How
The World Factbook, 2004, reports that U.S.airports have the following number of meters of runways that are either paved or unpaved.Number of Airports Total Runway (meters) Paved Unpaved More than 3047 188 1 2438–3047 221 7 1524–2437 1375 160 914–1523 2383 1718 Less than 914 961 7843 Total
Saturday mornings are busy times at the Webster Aquatic Center. Swim lessons ranging from the Red Cross Level 2, Fundamental Aquatic Skills, through the Red Cross Level 6, Swimming and Skill Proficiency, are offered during two sessions.Number of People in Number of People in Level 10:00 AM Class
Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster.Gender Female Male Satisfied 80 55 Not Satisfied 120 45 One viewer is to be randomly selected from those surveyed.a. Find P(satisfied)b. Find P(satisfied female)c. Find P(satisfied male)
A box stored in a warehouse contains 100 units of a specific part, of which 10 are defective and 90 are nondefective. Three parts are selected without replacement. Construct a tree diagram representing the sample space.
Worldwide the rate of maternal deaths (a woman’s risk of dying from pregnancy and childbirth)is 1 in 233. By regions around the world this rate is as follows: North America—1 in 3700, Northern Europe—1 in 4000, Africa—1 in 16, Asia—1 in 65, and Latin America/Caribbean—1 in 130. Express
The odds against being dealt a contract bridge hand containing 13 cards of the same suit are 158,753,389,899 to 1. The odds against being dealt a royal flush while playing poker are 649,739 to 1.a. What is the probability of being dealt a contract bridge hand containing 13 cards all of the same
The NCAA men’s basketball season starts with 327 college teams all dreaming of making it to“the big dance” and attaining the National Championship.Sixty-four teams are selected for the tournament, and only one wins it all.a. What are the odds against a team being selected for the
The odds of the Patriots winning next year’s Super Bowl are 1 to 12.a. What is the probability the Patriots will win next year’s Super Bowl?b. What are the odds against the Patriots winning next year’s Super Bowl?
A chocolate kiss is to be tossed into the air and will be landing on a smooth hard surface.(Similar to tossing a coin or rolling dice.)a. What proportion of the time do you believe the kiss will land “point up” (as opposed to“point down” )?b. Let’s estimate the probability that a
Using a coin, perform the experiment discussed on pages 213–214. Toss a coin 10 times, observe the number of heads (or put 10 coins in a cup, shake and dump them into a box, and use each toss for a block of 10), and record the results.Repeat until you have 200 tosses. Chart and graph the data as
Use a computer (or a random-number table)to simulate 200 trials of the experiment described in Exercise 4.35: the tossing of a penny and the rolling of a die. Let 1 H and 2 T for the penny, and 1, 2, 3, 4, 5, 6 for the die. Report your results using a cross-tabulated table showing the frequency
Use a computer (or a random-number table) to simulate the experiment described in Exercise 4.33;x is an integer 1 to 5, and y is an integer 1 to 4. Generate a list of 100 random x values and 100 y values.List the resulting 100 ordered pairs of integers.a. Find the relative frequency for x 2.b.
A computer generates (in random fashion)pairs of integers. The first integer is between 1 and 5, inclusive, and the second is between 1 and 4, inclusive.a. Represent the sample space as a tree diagram.b. List your outcomes as ordered pairs, with x as the first integer and y as the second integer.
a. Explain what is meant by the statement:“When a single die is rolled, the probability of a 1 is 16.”b. Explain what is meant by the statement:“When one coin is tossed one time, there is a 50-50 chance of getting a tail.”
A transportation engineer in charge of a new traffic-control system expresses the subjective probability that the system functions correctly 99 times as often as it malfunctions.a. Based on this belief, what is the probability that the system functions properly?b. Based on this belief, what is the
Let x be the success rating of a new television show. The following table lists the subjective probabilities assigned to each x for a particular new show by three different media critics. Which of these sets of probabilities are inappropriate because they violate a basic rule of probability?
Researchers have for a long time been interested in the relationship between cigarette smoking and lung cancer. The following table shows the percentages of adult females observed in a recent study.Smokes Does Not Smoke Gets Cancer 0.06 0.03 Does Not Get Cancer 0.15 0.76a. Display the information
A group of files in a medical clinic classifies the patients by gender and by type of diabetes(type 1 or type 2). The groupings may be shown as follows. The table gives the number in each classification.Type of Diabetes Gender 1 2 Male 30 15 Female 35 20a. Display the information on this 2 2 table
Three coins are tossed, and the number of heads observed is recorded. Find the probability for each of the possible results: 0H, 1H, 2H, and 3H.
A box contains one each of $1, $5, $10, and$20 bills.a. One is selected at random; list the sample space.b. Two bills are drawn at random (without replacement);list the sample space as a tree diagram.
An experiment consists of drawing one marble from a box that contains a mixture of red, yellow, and green marbles. There are at least two marbles of each color.a. List the sample space.b. Can we be sure that each outcome in the sample space in part a is equally likely? Explain.c. If two marbles are
The 12 face cards (4 jacks, 4 queens, and 4 kings) are removed from a regular deck of playing cards, and then one card is selected from this set of face cards. List the sample space for this experiment.
Take two dice (one white and one colored)and roll them 50 times, recording the results as ordered pairs [(white, color); for example, (3, 5) represents 3 on the white die and 5 on the colored die]. (You could simulate these 50 rolls using a random-number table or a computer.) Then calculate each
Two dice are rolled. Find the probabilities in parts b–e. Use the sample space given in Example 4.2 (pp. 208–209).a. Why is the set {2, 3, 4, . . . , 12} not a useful sample space?b. P(white die is an odd number)c. P(sum is 6)d. P(both dice show odd numbers)e. P(number on black die is larger
A pair of dice is to be rolled. In Example 4.2, the probability for each of the possible sums was discussed and three of the probabilities, P(2), P(3), and P(4), were found. Find the probability for each of the remaining sums of two dice: P(5), P(6), P(7), P(8), P(9), P(10), P(11), and P(12).
One single-digit number is to be selected randomly.List the sample space.
The two professional football coaches who won the most games during their careers were Don Shula and George Halas. Shula’s teams (Colts and Dolphins) won 347 games (a 347-173-6 record) and tied 6 of the 526 games that he coached, whereas Halas’s team (Bears) won 324 games (a 324-151-31 record)
In September 2004, the American Payroll Association reported the results of their National Payroll Week 2004 Survey. One of the questions asked about annual household income.Annual Household Income Number Percentage Less than $15,000 423 1.9%$15,001–$30,000 2225 9.8%$30,001–$50,000 5394
Webster Aquatic Center offers various levels of swimming lessons year-round. The March 2005 Monday and Wednesday evening lessons included instructions from Water Babies through Adults.The number in each classification is given in the table that follows.Swim Lesson Types No. of Participants Water
Millions of people ride railroads every year.The National Association of Railroad Passengers provides the following figures for railroad ridership in 2004.Rail System Riders (millions)Amtrak system 25.0 Northeast Corridor 14.2 Intercity West 10.8 Source: National Association of Railroad

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