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

If you were given a small bag of M&M’s with 40 candies in it, using the percentages in Table 4.2, how many of each color would you “expect” to find? Table 4.2, Color Percent Brown........ 13.2 Yellow ........ 16.2 Red........ 14.7 Blue ........ 21.8 Orange........
Demonstrates the law of large numbers and also allows you to see if you have psychic powers. Repeat the simulations at least 50 times, guessing between picking either a red card or a black card from a deck of cards. a. What proportion of the time did you guess correctly? b. As you made more and
An experiment consists of two trials. The first is tossing a penny and observing whether it lands with heads or tails facing up; the second is rolling a die and observing a 1, 2, 3, 4, 5, or 6. a. Construct the sample space using a tree diagram. b. List your outcomes as ordered pairs, with the
Use a computer (or a random number table) to simulate 200 trials of the experiment described in Exercise 4.31: 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
Using a coin, perform the experiment discussed on pages 180–181. 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
A box contains marbles of five different colors: red, green, blue, yellow, and purple. There is an equal number of each color. Assign probabilities to each color in the sample space
Suppose a box of marbles contains equal numbers of red marbles and yellow marbles but twice as many green marbles as red marbles. Draw one marble from the box and observe its color. Assign probabilities to the elements in the sample space.
If four times as many students pass a statistics course as those who fail and one statistics student is selected at random, what is the probability that the student will pass statistics?
Events A, B, and C are defined on sample space S. Their corresponding sets of sample points do not intersect, and their union is S. Furthermore, event B is twice as likely to occur as event A, and event C is twice as likely to occur as event B. Determine the probability of each of the three events.
Just as there are bad graphs (as seen in Section 2.7), there are bad charts€”charts that are misleading and hard to read. MADD reported the following data about the 6764 holiday traffic fatalities that occurred in 2002.What is wrong with the numbers on this chart?a. The column totals are
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. Sixtyfive teams are selected for the tournament and only one wins it all. a. What are the odds against a team being selected for the
Alan Garole was a jockey at Saratoga Springs Raceway during the 7/23/08 to 9/1/08 season. He had 195 starts, with 39 first places, 17 second places, and 28 third places. If all the 2008 racing season conditions had held for Alan Garole at the beginning of the 2009 season, what would have been: a.
Many young men aspire to become professional athletes. Only a few make it to the big time, as indicated in the table. Student-Athletes Baseball High School Student-Athletes......... 470,671 High School Senior Student-Athletes..... 134,477 NCAA Student-Athletes ............ 28,767 NCAA
Many young women aspire to become professional athletes. Only a few make it to the big time, as indicated in the table. Student-Athletes Women’s Basketball High School Student-Athletes...... 452,929 High School Senior Student-Athletes...... 129,408 NCAA Student-Athletes ..........
A bowl contains four kinds of identical-looking, foilwrapped, chocolate egg-shaped candies. All but 50 of them are milk chocolate, all but 50 are dark chocolate, all but 50 are semi-sweet chocolate, and all but 60 are white chocolate. a. How many candies are there in the bowl? b. How many of each
A bowl contains 100 identical-looking, foilwrapped, chocolate egg-shaped candies of four kinds. The candies are either milk or dark chocolate with either a nut or a raisin filling. All but 40 of them are milk chocolate, all but 56 are nut, and all but 29 are nut-filled or milk chocolate. a. How
Classify each of the following as a probability or a statistics problem: a. Determining whether a new drug shortens the recovery time from a certain illness b. Determining the chance that heads will result when a coin is tossed c. Determining the amount of waiting time required to check out at a
Classify each of the following as a probability or a statistics problem: a. Determining how long it takes to handle a typical telephone inquiry at a real estate office b. Determining the length of life for the 100-watt light bulbs a company produces c. Determining the chance that a blue ball will
Three hundred viewers were asked if they were satisfied with the TV coverage of a recent disaster.One viewer is to be randomly selected from those surveyed. a. Find P(satisfied). c. Find P(S male). b. Find P(S female).
Saturday mornings are busy times at the Webster Aquatic Center. Swim lessons ranging from Red Cross Level 2, Fundamental Aquatic Skills, through Red Cross Level 6, Swimming and Skill Proficiency, are offered during two sessions.Lauren, the program coordinator, is going to randomly select one
The World Factbook, 2008, reports that U.S. airports have the following numbers of meters of runways that are either paved or unpaved.If one of these airports is selected at random for inspection, what is the probability that it will have a. paved runways? b. 914 to 2437 meters of runway? c. less
During the Spring 2009 semester at Monroe Community College, a random sample of students was questioned on their knowledge of the meaning of €œsustainability.€ The primary motivation for the survey was to investigate how interested students might be in a Sustainability
A USA Today article, €œYum 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 of PepsiCo, has been
In 2007, data from two Youth Risk Behavior Surveys were analyzed to investigate seatbelt use among high school students ages 16 or older. The results were published in the September 2008 issue of American Journal of Preventive Medicine. Results (in percents) include the table that follows: If one
The American Community Survey reported its findings about workers€™ principal means of transportation to work during 2007.a. The column total is not included because it would be a meaningless value. Examine the table and explain why. One person is to be selected and asked additional
The five most popular colors for sport/compact cars manufactured during the 2006 model year in North America are reported here in percentages.a. Why does the column of percentages not total 100%? b. Why are all probabilities based on this table conditional? What is that condition? c. Did your
If P (A) = 0.4, P(B) = 0.5 and P(A and B) =0.7, Find P(A or B).
If P (A) = 0.4, P(B) = 0.9 and P(A and B) =0.1, Find P(A or B).
The entertainment sports industry employs athletes, coaches, referees, and related workers. Of these, 0.37 work part time and 0.50 earn more than $20,540 annually. If 0.32 of these employees work full time and earn more than $20,540, what proportion of the industry’s employees are full time or
Jason attends his high school reunion. Of the attendees, 50% are female. Common knowledge has it that 88% of people are right-handed. Being a left handed male, Jason knows that of a given crowd, only approximately 6% are left-handed males. If Jason talks to the first person he meets at the reunion,
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
“Is my class watching too much television on school nights?”This was a question that Mrs. Gordon wondered with respect to her seventh graders. She did a quick poll in class and found the following results: Hours Number 0........ 2 1.......... 3 2.......... 2 3.......... 0 4..........
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
A and B are events defined on a sample space, with P(A) = 0.7 and P(B0A) = 0.4. Find P(A and B)
A and B are events defined on a sample space, with P(A) = 0.7 and P(B0A) = 0.4. Find P(A and B)
A and B are events defined on a sample space, with P (A) = 0.6 and P (A and B) = 0. Find P(B|A).
A and B are events defined on a sample space, with P(B) = 0.5 and P(A and B) = 0.4 Find P(A|B)
It is known that steroids give users an advantage in athletic contests, but it is also known that steroid use is banned in athletes. As a result, a steroid testing program has been instituted and athletes are randomly tested. The test procedures are believed to be equally effective on both users
Juan lives in a large city and commutes to work daily by subway or by taxi. He takes the subway 80% of the time because it costs less, and he takes a taxi the other 20% of the time. When taking the subway, he arrives at work on time 70% of the time, whereas he makes it on time 90% of the time when
Nobody likes paying taxes, but cheating 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 doing so when audited, find the probability
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 get 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?
Find the probability of winning $5 if you play the carnival game described in Example 4.14. 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
4.8Webster Aquatic Center offers various levels of swim lessons year-round. The September 2008 Monday and Wednesday evening lessons included instructions for Water Babies through Adults. The number in each classification is given in the table that follows. Swim Lesson Types No. of
Suppose the rules for the carnival game in Example 4.14 are 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 4.79, listing the probabilities for the game when played “with replacement.” b. What is the
Suppose that A and B are events defined on a common sample space and that the following probabilities are known: P(A) = 0.3 P(B) = 0.4 and P (A/B) = 0.2 Find P (A or B).
Suppose that A and B are events defined on a common sample space and that the following probabilities are known P (A or B) = 0.7, P(b) = 0.5, and P (A,B) = 0.2 Find P(A)
Suppose that A and B are events defined on a common sample space and that the following probabilities are known: P(A) =0.4 P(B) = 0.3 and P(A or B) = 0.66. Find 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) 24, and P (A,B) = 0.4. Find P (A or B)
Given P (A or B) = 1.0, P (A and B) = 0.7 and P () = 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 () = 0.3 FIND: a. P(B) b. P(A) c. P (A|B)
The probability of A is 0.5.The conditional probability that A occurs given that B occurs is 0.25. The conditional probability that B occurs given that A occurs is 0.2. a. What is the probability that B occurs? b. What is the conditional probability that B does not occur given that A does not occur?
The probability of C is 0.4.The conditional probability that C occurs given that D occurs is 0.5. The conditional probability that C occurs given that D does not occur is 0.25. a. What is the probability that D occurs? b. What is the conditional probability that D occurs given that C occurs?
Determine whether each of the following pairs of events is mutually exclusive. a. Five coins are tossed: “one head is observed,” “at least one head is observed.” b. A salesperson calls on a client and makes a sale: “the sale exceeds $100,” “the sale exceeds $1000.” c. One student is
The table here shows the average number of births per day in the United States as reported by the CDC (Centers for Disease Control). Based on this information, what is the probability that one baby identified at random was: a. Born on a Monday? b. Born on a weekend? c. Born on a Tuesday or
Determine whether each of the following sets of events is mutually exclusive. a. Five coins are tossed: “no more than one head is observed,” “two heads are observed,” “three or more heads are observed.” b. A salesperson calls on a client and makes a sale: the amount of the sale is
If P(A) = 0.3 and P(B) = 0.4 and if A and B are mutually exclusive events, find:
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
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).
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
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 2009 alone, 283 people participated in various forms of lessons.If one swimmer was selected at random from the July participants: a. Are the events the
Refer to the chart accompanying “USA and Its Automobiles” on page 230. a. What percentage of households have three vehicles? b. What number of vehicles per household has the highest likelihood? c. What variable could be used to describe all eight of the events shown on the chart? d. Are the
A USA Today Snapshot titled “What women ‘splurge’ on” (July 21, 2009) reported that 34% of women said “shoes”; 22% said “handbags”; 15% said “work clothing”; 12% said “formal wear”; and 10% said “jewelry.” a. What is the variable involved, and what are the possible
Verify whether or not each of the following is a probability function. State your conclusion and explain. a. f (x) = 3x/8x for x _ 1, 2, 3, 4 b. f (x) _ 0.125, for x _ 0, 1, 2, 3 and f (x) _ 0.25, for x _ 4, 5 c. f (x) _ (7 - x)/28, for x _ 0, 1, 2, 3, 4, 5, 6, 7 d. f (x) _ (x2 + 1)/60, for x _ 0,
The number of ships to arrive at a harbor on any given day is a random variable represented by x. The probability distribution for x is as follows:Find the probability of the following for any a given day: a. Exactly 14 ships arrive. b. At least 12 ships arrive. c. At most 11 ships arrive.
€œHow many TVs are there in your household?€ was one of the questions on a questionnaire sent to 5000 people in Japan. The collected data resulted in the following distribution:a. What percentage of the households have at least one television? b. What percentage of the
Patients who have hip-replacement surgery experience pain the first day after surgery. Typically, the pain is measured on a subjective scale using values of 1 to 5.Let x represent the random variable, the pain score as determined by a patient. The probability distribution for x is believed to be:a.
The coffee consumption per capita in the United States is approximately 1.9 cups per day for men and 1.4 cups for women. The number of cups consumed per day, x, by women coffee drinkers is expressed as the accompanying distribution.a. Is this a discrete probability distribution? Explain. b. Draw a
A doctor knows from experience that 10% of the patients to whom she gives a certain drug will have undesirable side effects. Find the probabilities that among the 10 patients to whom she gives the drug: a. At most two will have undesirable side effects. b. At least two will have undesirable side
In a recent survey of women, 90% admitted that they had never looked at a copy of Vogue magazine. Assuming that this is accurate information, what is the probability that a random sample of three women will show that fewer than two have read the magazine?
Of those seeking a driver’s license, 70% admitted that they would not report someone if he or she copied some answers during the written exam. You have just entered the room and see 10 people waiting to take the written exam. What is the probability that if copying took place, 5 of the 10 would
The engines on an airliner operate independently. The probability that an individual engine operates for a given trip is 0.95. A plane will be able to complete a trip successfully if at least one-half of its engines operate for the entire trip. Determine whether a four-engine or a two engine plane
The Pew Internet & American Life Project found that nearly 70% of “wired” senior citizens go online every day. In a randomly selected group of 15 “wired” senior citizens: a. What is the probability that more than four will say they go online every day? b. What is the probability that
There are 750 players on the active rosters of the 30 Major League Baseball teams. A random sample of 15 players is to be selected and tested for use of illegal drugs. a. If 5% of all the players are using illegal drugs at the time of the test, what is the probability that 1 or more players test
A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are selected without replacement, and x is the number of defective items in the sample of two. Explain why x is not a binomial random variable.
A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defectives in the sample of two. Explain why x is a binomial random variable.
A large shipment of radios is accepted upon delivery if an inspection of 10 randomly selected radios yields no more than 1 defective radio. a. Find the probability that this shipment is accepted if 5% of the total shipment is defective. b. Find the probability that this shipment is not accepted if
The town council has nine members. A proposal to establish a new industry in this town has been tabled, and all proposals must have at least two-thirds of the votes to be accepted. If we know that two members of the town council are opposed and that the others randomly vote “in favor” and
The state bridge design engineer has devised a plan to repair North Carolina’s 4706 bridges that are currently listed as being in either poor or fair condition. The state has a total of 13,268 bridges. Before the governor will include the cost of this plan in his budget, he has decided to
A discrete random variable has a standard deviation equal to 10 and a mean equal to 50. Find ∑x2P(x)
A binomial random variable is based on n _ 20 and p _ 0.4. Find ∑x2P(x)
If you could stop time and live forever in good health, what age would you pick? Answers to this question were reported in a USA Today Snapshot. The average ideal age for each age group is listed in the following table; the average ideal age for all adults was found to be 41. Interestingly, those
In a germination trial, 50 seeds were planted in each of 40 rows. The number of seeds germinating in each row was recorded as listed in the following table.a. Use the preceding frequency distribution table to determine the observed rate of germination for these seeds. b. The binomial probability
In another germination experiment involving old seed, 50 rows of seeds were planted.The number of seeds germinating in each row were recorded in the following table (each row contained the same number of seeds).a. What probability distribution (or function) would be helpful in modeling the variable
A business firm is considering two investments. It will choose the one that promises the greater payoff. Which of the investments should it accept? (Let the mean profit measure the payoff.)
Bill has completed a 10-question multiple-choice test on which he answered 7 questions correctly. Each question had one correct answer to be chosen from five alternatives. Bill says that he answered the test by randomly guessing the answers without reading the questions or answers. a. Define the
A random variable that can assume any one of the integer values 1, 2, . . . , n with equal probabilities of is said to have a uniform distribution. The probability function is written P(x) _ 1/n for x _ 1, 2, 3,. , n. Show that µ = n+ ½.
a. Express P(x) = 1/6 for x = 1, 2, 3, 4, 5, 6, in distribution form. b. Construct a histogram of the probability distribution P(x) = 1/6 for x = 1, 2, 3, 4, 5, 6 c. Describe the shape of the histogram in part b.
a. Explain how the various values of x in a probability distribution form a set of mutually exclusive events. b. Explain how the various values of x in a probability distribution form a set of “all-inclusive” events.
Test the following function to determine whether it is a probability function. If it is not, try to make it into a probability function. R(x) _ 0.2, for x _ 0, 1, 2, 3, 4 a. List the distribution of probabilities. b. Sketch a histogram.
Test the following function to determine whether it is a probability function.a. List the probability distribution. b. Sketch a histogram.
Test the following function to determine whether it is a probability function. If it is not, try to make it into a probability function.a. List the distribution of probabilities and sketch a histogram. b. Do you recognize S(x)? If so, identify it.
Census data are often used to obtain probability distributions for various random variables. Census data for families in a particular state with a combined income of $50,000 or more show that 20% of these families have no children, 30% have one child, 40% have two children, and 10% have three
In a USA Today Snapshot (June 1, 2009), the following statistics were reported on the number of hours of sleep that adults get.a. Are there any other values that the number of hours can attain? b. Explain why the total of the percentages is not 100%. c. Is this a discrete probability distribution?
Verify that formulas (5.3a) and (5.3b) are equivalent to formula (5.2).
a. Form the probability distribution table for P(x) = x/6 for x = 1, 2, 3. b. Find the extensions xP(x) and for each x. c. Find ∑[xP(x) and ∑ [x2P(x)] d. Find the mean for P(x) \= x/6 for x = 1, 2, 3 e. Find the variance for P(x) = x/6 for x = 1,2,3. f. Find the standard deviation for P(x) =
Given the probability function P(x) = 5 – x/ 10 for x _ 1, 2, 3, 4 find the mean and standard deviation.
Given the probability function R(x) _ 0.2 , for x _ 0, 1, 2, 3, 4 , find the mean and standard deviation.
The number of ships to arrive at a harbor on any given day is a random variable represented by x. The probability distribution for x is as follows:Find the mean and standard deviation of the number of ships that arrive at a harbor on a given day.
The College Board website provides much information for students, parents, and professionals with respect to the many aspects involved in Advanced Placement (AP) courses and exams. One particular annual report provides the percent of students who obtain each of the possible AP grades (1 through 5).
The number of children per household, x, in the United States in 2008 is expressed as a probability distribution here.a. Is this a discrete probability distribution? Explain. b. Draw a histogram for the distribution of x, the number of children per household. c. Replacing €œ 5 + with

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