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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions

When was the last time you saw your doctor? That question was asked for the survey summarized in the following table.a. Find the marginal totals. b. Express the frequencies as percentages of the grand total. c. Express the frequencies as percentages of each age group€™s marginal
Part of quality control is keeping track of what is occurring. The following contingency table shows the number of rejected castings last month categorized by their cause and the work shift during which they occurred.a. Find the marginal totals. b. Express the numbers as percentages of the grand
Determine whether each of the following questions requires correlation analysis or regression analysis to obtain an answer. a. Is there a correlation between the grades a student attained in high school and the grades he or she attained in college? b. What is the relationship between the weight of
An automobile owner records the number of gallons of gasoline, x, required to fill the gasoline tank and the number of miles traveled, y, between fill-ups. a. If she does a correlation analysis on the data, what would be her purpose and what would be the nature of her results? b. If she does a
Display these rates as two dotplots using the same scale; compare means and medians.
These data were generated using the equation y = 2x + 1A scatter diagram of the data results in five points that fall perfectly on a straight line. Find the correlation coefficient and the equation of the line of best fit.
Consider this set of bivariate data:a. Draw a scatter diagram. b. Calculate the correlation coefficient. c. Calculate the line of best fit.
Start with the point (5, 5) and add at least four ordered pairs, (x, y), to make a set of ordered pairs that display the following properties. Show that your sample satisfies the requirements. a. The correlation of x and y is 0.0. b. The correlation of x and y is +1.0 c. The correlation of x and y
A scatter diagram is drawn showing the data for x and y, two normally distributed variables. The data fall within the intervals 20 ≤ x ≤ 40 and 60 ≤ y ≤ 100 Where would you expect to find the data on the scatter diagram, if: a. The correlation coefficient is 0.0 b. The correlation
Start with the point (5, 5) and add at least four ordered pairs, (x, y), to make a set of ordered pairs that display the following properties. Show that your sample satisfies the requirements. a. The correlation of x and y is between + 0.9 and _1.0 and the slope of the line of best fit is 0.5. b.
A biological study of a minnow called the blacknose dace* was conducted. The length, y (in millimeters), and the age, x (to the nearest year), were recorded.a. Draw a scatter diagram of these data. b. Calculate the correlation coefficient. c. Find the equation of the line of best fit. d. Explain
The following data are a sample of the ages and the asking prices for used Honda Accords that were listed on AutoTrader.com on March 10, 2005:a. Draw a scatter diagram. b. Calculate the equation of the line of best fit. c. Graph the line of best fit on the scatter diagram. d. Predict the average
The sound of crickets chirping is a welcome summer night€™s sound. In fact, those chirping crickets may be telling you the temperature. In the book The Song of Insects, George W. Pierce, a Harvard physics professor, presented real data relating the number of chirps per second, x, for
Lakes are bodies of water surrounded by land and may include seas. The accompanying table lists the areas and maximum depths of 32 lakes throughout the world.a. Draw a scatter diagram showing area, x, and maximum depth, y, for the lakes.b. Find the linear correlation coefficient between area and
Wildlife populations are monitored with aerial photographs.The number of animals and their locations relative to areas inhabited by the human population are useful information. Sometimes it is possible to monitor the physical characteristics of the animals. The length of an alligator can be
The 2007 Current Population Survey reported the following results on U.S. annual household income (in thousands). The survey is a joint effort between the Census Bureau and the Bureau of Labor Statistics.Suppose one household is to be selected at random for a follow-up interview. Find the
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.If one player
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
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%
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 die b. Drawing a “spade” from a regular deck of playing cards and then drawing another “spade” from the same deck without
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
A and B are independent events, and P(A) = 0.7 and P(B) = 0.4. Find P(A and B).
A and B are independent events, and P(A) = 0.5 and P(B) = 0.8 .Find P(A and B).
A and B are independent events P(A)= 0.6, and P(A and B) = 0.3 .Find P(B).
A and B are independent events, and and P(A) = 0.4 and P(A and B).= 0.5. Find P(B).
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(B0A) c. P(A0B)
There is a large variation in price for private fouryear colleges in the United States. The average 2007€“2008 tuition and fees ranged from $3,000 to over $36,000 annually, according to CollegeBoard (www. collegeboard.com/). The distribution of full-time undergraduates at private
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|0A) c. Are A and B independent?
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?
One student is selected at random from a group of 200 students known to consist of 140 full-time (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 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 B b. A and C c. B and C
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
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
The U.S. space program has a history 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 the reliability of all its components. Each of the six joints in the space shuttle
In a 2008 study by Experian Automotive, it was found that the average number of vehicles per household in the United States is 2.28 vehicles.The results also showed that nearly 35% of households have three or more vehicles. www.autospies.com/ a. If two U.S. households are randomly selected, find
A box contains one each of $1, $5, $10, and $20 bills. a. One bill 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.
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 that you receive both scholarships is 0.15, and the probability that you get at least one of the scholarships is
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 person has a history of making the right
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?
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
A box contains 25 parts, of which 3 are defective and 22 are non-defective. 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)
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.
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
G) = 0.5 P(H) = 0.4. and P(G and H) = 0.1(see the diagram).a. Find P(G, H)b. Find P(H, G).c. Find P( H ).d. Find P(G or H).e. Find P(G or H).f. Are events G and H mutually exclusive? Explain.g. Are events G and H independent? Explain.
One single-digit number is selected randomly. a. List the sample space. b. What is the probability of each single digit? c. What is the probability of an even number?
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.
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.
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
One thousand employees at the Russell Microprocessor Company were polled about worker satisfaction. One employee is selected at random.a. Find the probability that an unskilled worker is satisfied with work. b. Find the probability that a skilled female employee is satisfied with work. c. Is
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
The U.S. Department of Transportation and the Federal Motor Carrier Safety Administration produce an annual report on various traffic violations. There were 2092 €œmoving violations€ in the state of New York in 2008, as described in the following table.If one violation is
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.a. Verify the percentages reported in the table. If one person is picked at random from all the people represented in the table, what is the probability
The Federal Highway Administration periodically tracks the number of licensed vehicle drivers by sex and by age. The following table shows the results of the administration€™sfindings in 2007:Suppose you encountered a driver of a vehicle at random. Find the probabilities of the following
Let’s assume there are three traffic lights between your house and a friend’s house. As you arrive at each light, it may be red (R) or green (G). a. List the sample space showing all possible sequences of red and green lights that could occur on a trip from your house to your friend’s. (RGG
A single die is rolled. What is the probability that the number on top is the following? a. A 3 b. An odd number c. A number less than 5 d. A number no greater than 3
Assuming that a woman is equally likely to bear a boy or a girl, use a tree diagram to compute the probability that a four-child family consists of one boy and three girls.
A coin is flipped three times. a. Draw a tree diagram that represents all possible outcomes. b. Identify all branches that represent the event “exactly one head occurred.” c. Find the probability of “exactly one head occurred.”
A recent survey of New York State families asked about their vacation habits. The accompanying two-way table shows the number of families according to where they live (rural, suburban, urban) and the length of their last vacation (1€“7 days, 8 days or more).If one family is selected at
The age and gender demographics for the Fall 2008 Monroe Community College full-time students are outlined in the table below.If one of these students is selected at random, what is the probability that the student is a. a male? b. between 20 and 24 years of age? c. a female and 30 and over? d. a
This bar graph shows the number of registered automobiles in each of several countries.a. Name at least two countries not included in the information.b. Why are all probabilities resulting from this information conditional probabilities? Based on the information in the accompanying graph:c. What
Probabilities for events A, B, and C are distributed as shown in the figure. Find:a. P(A and B)b. P(A or C)c. P(A0 C)
Show that if event A is a subset of event B, then P(A or B) =P(B).
A shipment of grapefruit arrived containing the following proportions of types: 10% pink seedless, 20% white seedless, 30% pink with seeds, and 40% white with seeds. A grapefruit is selected at random from the shipment.Find the probability of these events: a. It is seedless. b. It is white. c. It
A bowl contains two kinds of identical-looking, foilwrapped, chocolate egg-shaped candies. All but 42 of them are milk chocolate and all but 35 are dark chocolate. a. How many of each kind are in the bowl? b. How many candies are there in the bowl? c. If one chocolate is selected at random, what is
Suppose that when a job candidate interviews for a job at RJB Enterprises, the probability that he or she will want the job (A) after the interview is 0.68. Also, the probability that RJB will want the candidate (B) is 0.36. The probability P(A0 B) is 0.88 a. Find P(A and B). b. Find P(B 0A) c. Are
The probability that thunderstorms are in the vicinity of a particular Midwestern airport on an August day is 0.70. When thunderstorms are in the vicinity, the probability that an airplane lands on time is 0.80. Find the probability that thunderstorms are in the vicinity and that the plane lands on
Tires salvaged from a train wreck are on sale at the Getrich Tire Company. Of the 15 tires offered in the sale, 5 have suffered internal damage and the remaining 10 are damage free. You randomly selected and purchased two of these tires. a. What is the probability that the tires you purchased are
According to automobile accident statistics, one out of every six accidents results in an insurance claim of $100 or less in property damage.Three cars insured by an insurance company are involved in different accidents. Consider these two events: A: The majority of claims exceed $100. B: Exactly
A testing organization wishes to rate a particular brand of television. Six TVs are selected at random from stock. If nothing is found wrong with any of the six, the brand is judged satisfactory. a. What is the probability that the brand will be rated satisfactory if 10% of the TVs actually are
Suppose a certain ophthalmic trait is associated with eye color. Three hundred randomly selected individuals are studied, with results given in the following table.a. What is the probability that a person selected at random has blue eyes? b. What is the probability that a person selected at random
As listed in The World Factbook, 2009, the age structure of the U.S. population is shown in the table.If one U.S. citizen were to be selected at random from this population, what is the probability that the person selected is a. female? b. 0€“14 years old? c. male and 15€“64
The following table shows the sentiments of 2500 wage-earning employees at the Spruce Company on a proposal to emphasize fringe benefits rather than wage increases during their impending contract discussions.a. Calculate the probability that an employee selected at random from this group will be
Events R and S are defined on a sample space. If P(R) = 0.2 and P(S) = 0.5 explain why each of the following statements is either true or false: a. If R and S are mutually exclusive, then P(R or S) = 0.10 b. If R and S are independent, then P(R or S) = 0.6 c. If R and S are mutually exclusive,
A bowl contains three kinds of identical-looking, foil-wrapped, chocolate egg-shaped candies. All but 50 of them are milk chocolate, all but 50 are dark chocolate, and all but 50 are semi-sweet chocolate. a. How many candies are there in the bowl? b. How many of each kind are in the bowl? c. If one
It is believed that 3% of a clinic’s patients have cancer. A particular blood test yields a positive result for 98% of patients with cancer, but it also shows positive for 4% of patients who do not have cancer. One patient is chosen at random from the clinic’s patient list and is tested. What
Box 1 contains two red balls and three green balls, and Box 2 contains four red balls and one green ball. One ball is randomly selected from Box 1 and placed in Box 2. Then one ball is randomly selected from Box 2.What is the probability that the ball selected from Box 2 is green?
Salespersons Adams and Jones call on three and four customers, respectively, on a given day. Adams could make0, 1, 2, or 3 sales, whereas Jones could make 0, 1, 2, 3, or 4 sales. The sample space listing the number of possible sales for each person on a given day is shown in the table. (3, 1 stands
Alex, Bill, and Chen each, in turn, toss a balanced coin. The first one to throw a head wins. a. What are their respective chances of winning if each tosses only one time? b. What are their respective chances of winning if they continue, given a maximum of two tosses each?
Coin A is loaded in such a way that P(heads) is 0.6. Coin B is a balanced coin. Both coins are tossed. Find: a. The sample space that represents this experiment; assign a probability measure to each outcome b. P(both show heads) c. P(exactly one head shows) d. P(neither coin shows a head) e. P(both
Professor French forgets to set his alarm with a probability of 0.3. If he sets the alarm, it rings with a probability of 0.8. If the alarm rings, it wakes him on time to make his first class with a probability of 0.9. If the alarm does not ring, he wakes in time for his first class with a
The probability that a certain door is locked is 0.6. The key to the door is one of five unidentified keys hanging on a key rack. You randomly select two keys before approaching the door. What is the probability that you can open the door without returning for another key?
Your local art museum has planned next year’s 52-week calendar by scheduling a mixture of 1-week and 2-week shows that feature the works of 22 painters and 20 sculptors. There is a showing scheduled for every week of the year, and only one artist is featured at a time. There are 42 different
A two-page typed report contains an error on one of the pages. Two proofreaders review the copy. Each has an 80% chance of catching the error.What is the probability that the error will be identified in the following cases? a. Each reads a different page. b. They each read both pages. c. The first
In sports, championships are often decided by two teams playing in a championship series. Often the fans of the losing team claim they were unlucky and their team is actually the better team. Suppose Team A is the better team, and the probability it will defeat Team B in any one game is 0.6. a.
Use either the random number table (Appendix B), a calculator, or a computer (see p. 90) to simulate the following: a. The rolling of a die 50 times; express your results as relative frequencies. b. The tossing of a coin 100 times; express your results as relative frequencies.
A woman and a man (unrelated) each has two children. At least one of the woman’s children is a boy, and the man’s older child is a boy. Is the probability that the woman has two boys greater than, equal to, or less than the probability that the man has two boys? a. Demonstrate the truth of your
Three balanced coins are tossed simultaneously. Find the probability of obtaining three heads, given that at least one of the coins shows heads. a. Solve using an equally likely sample space. b. Solve using the formula for conditional probability.
Use either the random number table (Appendix B), a calculator, or a computer to simulate the random selection of 100 single-digit numbers, 0 through 9. a. List the 100 digits. b. Prepare a relative frequency distribution of the 100 digits. c. Prepare a relative frequency histogram of the
A pair of dice is to be rolled. In Example 4.3, 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).
a. Construct a bar graph showing the Table 4.2 percentages obtained from the 692 M&M’s. b. Based on your graph, which color M&M occurred most often? How does this show on your graph? c. Based on your graph, which color M&M occurred the least? How does this show on your graph?
Two dice are rolled. Find the probabilities in parts b–e. Use the sample space given in Example 4.3 (p. 175). 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 than
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
Use a random number table or a computer to simulate rolling a pair of dice 100 times. a. List the results of each roll as an ordered pair and a sum. b. Prepare an ungrouped frequency distribution and a histogram of the sums. c. Describe how these results compare with what you expect to occur when
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?
a. A balanced coin is tossed twice. List a sample space showing the possible outcomes. b. A biased coin (it favors heads in a ratio of 3 to 1) is tossed twice. List a sample space showing the possible outcomes.
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.a. Display the information on this 2 Ã— 2 table as a Venn diagram using
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.a. Display the information on this table as a Venn diagram using €œsmokes€ and
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 a Venn diagram.
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 a Venn diagram.
a. Explain what is meant by the statement: “When a single die is rolled, the probability of a 1 is .” 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.”

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