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elementary statistics

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

If the binomial (q p) is squared, the result is(q p)2 q2 2qp p2. For the binomial experiment with n 2, the probability of no successes in two trials is q2 (the first term in the expansion), the probability of one success in two trials is 2qp (the second term in the expansion), and the
Extended to overtime in a game 7 on the road in the 2002 NBA play-offs, the two-time defending champion Los Angeles Lakers did what they do best—thrived when the pressure was at its highest. Both of the Lakers’ star players had their chance at the foul line late in overtime.a. With 1:27 minutes
a. When using the exact binomial test (Applied Example 5.10, pp. 293–294), what is the interpretation of the situation when the calculated value of P is less than or equal to 0.05?b. When using the exact binomial test, what is the interpretation of the situation when the calculated value of P is
Harris Interactive conducted a survey for Tylenol PM asking U.S. drivers what they do if they are driving while drowsy. The results were reported in a USA Snapshot on January 18, 2005, with 40% of the respondents saying they “open the windows” to fight off sleep. Suppose that 35 U.S. drivers
Where does all that Halloween candy go?The October 2004 issue of Readers’ Digest quoted that “90% of parents admit taking Halloween candy from their children’s trick-or-treat bags.”The source of information was the National Confectioners Association. Suppose that 25 parents are interviewed.
The increase in Internet usage over the past few years has been phenomenal, as demonstrated by the February 2004 report from Pew Internet &American Life Project. The survey of Americans 65 or older (about 8 million adults) reported that 22%have access to the Internet. By contrast, 58% of 50-to
Use a computer to find the cumulative probabilities for all possible x values for a binomial experiment where n 45 and p 0.125.a. Explain why there are so many 1.000s listed.b. Explain what is represented by each number listed.MINITAB (Release 14)Choose: Calc Make Patterned Data Simple Set
Use a computer to find the probabilities for all possible x values for a binomial experiment where n 30 and p 0.35.MINITAB (Release 14)Choose: Calc Make Patterned Data Simple Set of Numbers Enter: Store patterned data in: C1 From first value: 0 To last value: 30 In steps of: 1 OK Continue
a. Use a calculator or computer to find the probability that x 3 in a binomial experiment where n 12 and p 0.30:P(x 3 B(12, 0.30)). (See Note about this notation on p. 292.)b. Use Table 5.8 to verify the answer in part a.
Of all mortgage foreclosures in the United States, 48% are caused by disability. People who are injured or ill cannot work—they then lose their jobs and thus their incomes. With no income, they cannot make their mortgage payment and the bank forecloses.Source: http://www.ricedelman.com 06.11.02
According to the USA Snapshot “Knowing drug addicts,” 45% of Americans know somebody who became addicted to a drug other than alcohol.Assuming this to be true, what is the probability of the following:a. Exactly 3 people of a random sample of 5 know someone who became addicted. Calculate the
Consider the manager of Steve’s Food Market as illustrated in Example 5.9. What would be the manager’s “risk” if he bought “better” eggs, say with P(bad) 0.01 using the “more than one”guarantee?
As a quality-control inspector for toy trucks, you have observed that 3% of the time, the wooden wheels are bored off-center. If six wooden wheels are used on each toy truck produced, what is the probability that a randomly selected toy truck has no off-center wheels?
St. Louis Cardinal baseball player Albert Pujols has a 3-year batting average (ratio of hits to at bats) of 0.334 for the 2002–2004 seasons. Suppose Pujols has five official times at bat during his next game. Assuming no extenuating circumstances and that the binomial model will produce
One-fourth of a certain breed of rabbits are born with long hair. What is the probability that in a litter of six rabbits, exactly three will have long hair? (Find the answer by using a formula.)
If boys and girls are equally likely to be born, what is the probability that in a randomly selected family of six children, there will be at least one boy? (Find the answer using a formula.)
A January 2005 survey of bikers, commissioned by the Progressive Group of Insurance Companies, showed that 40% of bikers have body art, such as tattoos and piercings. A group of 10 bikers are in the process of buying motorcycle insurance.Source:
Of the parts produced by a particular machine, 0.5% are defective. If a random sample of 10 parts produced by this machine contains 2 or more defective parts, the machine is shut down for repairs. Find the probability that the machine will be shut down for repairs based on this sampling plan.
The survival rate during a risky operation for patients with no other hope of survival is 80%.What is the probability that exactly four of the next five patients survive this operation?
In the biathlon event of the Olympic Games, a participant skis cross-country and on four intermittent occasions stops at a rifle range and shoots a set of five shots. If the center of the target is hit, no penalty points are assessed. If a particular man has a history of hitting the center of the
The Pew Internet & American Life Project produces reports that explore the impact of the Internet on many facets of our daily life, whether at home, school, or the office. In its January 2005 Tracking Survey, it found that more than 80% of 18- to 29-year-olds use the Internet. Consider a randomly
First graders who misbehave in school may be more likely to be regular smokers as young adults according to a new study presented in the July 2004 issue of the American Journal of Epidemiology.After following a group of U.S. first graders for 15 years, it was found that among those kids who had
According to the Federal Trade Commission, more than half of the 358,603 consumer fraud complaints in 2004 were Internet related—53% to be more accurate. In a group of 20 people who have filed a fraud complaint, what is the probability that exactly half are Internet related?
Of all the trees planted by a landscaping firm, 90% survive. What is the probability that 8 or more of the 10 trees they just planted will survive?(Find the answer by using a table.)
a. Calculate P(4) and P(5) for Example 5.8 on page 290.b. Verify that the six probabilities P(0), P(1), P(2), . . . , P(5) form a probability distribution.
Use the probability function for three coin tosses as demonstrated on page 289 and verify the probabilities for x 0, 2, and 3.
Draw a tree diagram picturing a binomial experiment of four trials.
The employees at a General Motors assembly plant are polled as they leave work. Each is asked,“What brand of automobile are you riding home in?” The random variable to be reported is the number of each brand mentioned. Is x a binomial random variable? Justify your answer.
Four cards are selected, one at a time, from a standard deck of 52 playing cards. Let x represent the number of aces drawn in the set of four cards.a. If this experiment is completed without replacement, explain why x is not a binomial random variable.b. If this experiment is completed with
A die is rolled 20 times, and the number of“fives” that occurred is reported as being the random variable. Explain why x is a binomial random variable.
A carton containing 100 T-shirts is inspected.Each T-shirt is rated “first quality” or “irregular.”After all 100 T-shirts have been inspected, the number of irregulars is reported as a random variable.Explain why x is a binomial random variable.
What does it mean for the trials to be independent in a binomial experiment?
State a very practical reason why the defective item in an industrial situation might be defined to be the “success” in a binomial experiment.
Identify the properties that make flipping a coin 50 times and keeping track of heads a binomial experiment.
Consider the four-question multiple-choice quiz presented at the beginning of this section (pp.284–287).a. Explain why the four questions represent four independent trials.b. Explain why the number 4 is multiplied into the P(x 1).c. In Answer 5 on page 287, where did 13 and 4 come from? Why
Every Tuesday, Jason’s Video has “roll-thedice”day. A customer may roll two fair dice and rent a second movie for an amount (in cents) determined by the numbers showing on the dice, the larger number first. For example, if the customer rolls a one and a five, a second movie may be rented for
a. Draw a histogram of the probability distribution for the single-digit random numbers 0, 1, 2, . . . , 9.b. Calculate the mean and standard deviation associated with the population of single-digit random numbers.c. Represent (1) the location of the mean on the histogram with a vertical line
Given the probability function R(x) 0.2 for x 0, 1, 2, 3, 4, find the mean and standard deviation.
Given the probability function P(x) for x 1, 2, 3, 4, find the mean and standard deviation.
If you find the sum of the x and the x2 columns on the extensions table, exactly what have you found?
a. Form the probability distribution table for P(x) , for x 1, 2, 3.b. Find the extensions xP(x) and x2P(x) for each x.c. Find [xP(x)] and [x2P(x)].d. Find the mean for P(x) , for x 1, 2, 3.e. Find the variance for P(x) , for x 1, 2, 3.f. Find the standard deviation for P(x) , for x
Verify that formulas (5.3a) and (5.3b) are equivalent to formula (5.2).
a. Use a computer (or random-number table) and generate a random sample of 100 observations drawn from the discrete probability population P(x) = 5-3/10, for x 1, 2, 3, 4. List the resulting sample.(Use the computer commands in Exercise 5.25; just change the arguments.)b. Form a relative
As part of a 2003 Consumer Preferences Report, the following information was gathered. It indicates the percentage, as a relative frequency, of new home customers who desired each outdoor feature as part of their new home. Is this a probability distribution? Explain.Outdoor Feature Percentage (Rel.
In February 2004, the Oregon’s Medically Needy Program Survey reported the following statistics pertaining to the medically needy population in their state. Due to budget cuts, the Medically Needy Program was eliminated. It had provided Medicare assistance to certain groups who were not eligible
How many colleges did you apply to other than the one in which are enrolled? This was just the question asked and illustrated in Applied Example 5.3, “Applying for Admission,” on page 276.a. Using the variable x, number of additional applications for admission completed, express the information
Is “a dog, man’s best friend”? One would think so with 60 million pet dogs nationwide. But how many friends are needed? In the USA Snapshot(February 22, 2005), the following statistics were reported.Number of Pet Dogs Percentage Number of Pet Dogs Percentage One 66 Four 3 Two 24 Five or more
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
Test the following function to determine whether it is a probability function.P(x) , for x 1, 2, 3, 4a. 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.R(x) 0.2 for x 0, 1, 2, 3, 4.a. List the distribution of probabilities.b. Sketch a histogram.
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.1 6 1 6
a. Express P(x) ; for x 1, 2, 3, 4, 5, 6, in distribution form.b. Construct a histogram of the probability distribution P(x) ; for x 1, 2, 3, 4, 5, 6.c. Describe the shape of the histogram in part b.
Express the tossing of one coin as a probability distribution of x, the number of heads occurring(that is, x 1 if a head occurs and x 0 if a tail occurs).
[EX05-012] 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 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,
A USA Today article titled “Electronic world swallows up kids’ time, study finds” (March 10, 2005) presented the following chart depicting the average amount of time 8- to 18-year-olds spend daily on various activities. The Kaiser Family Foundation had conducted the study of 2000 children in
A USA Snapshot titled “Are you getting a summer job?” (July 8, 2002) reported that 49% of high school students said, “Getting? I already have one”; 26% said, “Maybe. Depends on my cash situation”;and 25% said, “No! Nothing interferes with my beach time.”a. What is the variable
An archer shoots arrows at a bull’s-eye of a target and measures the distance from the center of the target to the arrow. Identify the random variable of interest, determine whether it is discrete or continuous, and list its possible values.
Above-average warmth extended over the east and southeast on January 13, 2005. The day’s forecasted high temperatures in four cities in the affected area were as follows.City Temperature City Temperature Burlington, VT 55°F Durham, NC 74°F Williamsburg, VA 74°F Augusta, GA 75°Fa. What is the
The staff at Fortune recently isolated what they considered to be the 100 best companies in America to work for. Many companies on the list were hiring last year. Those adding the most employees are listed here.Company New Jobs Company New Jobs Marriott International 3679 Booz Allen Hamilton 2463
A social worker is involved in a study about family structure. She obtains information regarding the number of children per family for a certain community from the census data. Identify the random variable of interest, determine whether it is discrete or continuous, and list its possible values.
a. The variables in Exercise 5.3 are either discrete or continuous. Which are they and why?b. Explain why the variable “number of dinner guests for Thanksgiving dinner” is discrete.c. Explain why the variable “number of miles to your grandmother’s house” is continuous.
a. Explain why the variable “number of saved telephone numbers on a person’s cell phone” is discrete.b. Explain why the variable “weight of a statistics textbook” is continuous.
Survey your classmates about the number of siblings they have and the length of the last conversation they had with their mother. Identify the two random variables of interest and list their possible values.
Refer to the graphic “Americans like their coffee!”to answer the following questions:a. What other statistical graph could be used to picture or display this information? Draw it.b. What other statistical methods could be used to describe this information?
Refer to the graphic “Americans like their coffee!”to answer the following questions:a. What percentage of adults do not drink any caffeinated beverages?b. What number of cups or cans of caffeinated beverages has the highest likelihood?c. What variable could be used to describe all five of the
Using complete sentences, describe the following in your own words:a. Mutually exclusive eventsb. Independent eventsc. The probability of an eventd. A conditional probability
Student A says that independence and mutually exclusive are basically the same thing;namely, both mean neither event has anything to do with the other one. Student B argues that although Student A’s statement has some truth in it, Student A has missed the point of these two properties. Student B
Janice wants to become a police officer. She must pass a physical exam and then a written exam. Records show that the probability of passing the physical exam is 0.85 and that once the physical is passed, the probability of passing the written exam is 0.60. What is the probability that Janice
Events E and F have probabilities P(E) 0.5, P(F) 0.4, and P(E and F) 0.2.a. Find P(E or F).b. Find P(E F).c. Are E and F mutually exclusive? Explain.d. Are E and F independent? Explain.d. Are G and H independent? Explain.
Events A and B are mutually exclusive and P(A) 0.4 and P(B) 0.3.a. Find P(A and B).b. Find P(A or B).c. Find P(A B).d. Are events A and B independent? Explain.
A computer is programmed to generate the eight single-digit integers 1, 2, 3, 4, 5, 6, 7, and 8 with equal frequency. Consider the experiment“the next integer generated” and these events:A: odd number, {1, 3, 5, 7}B: number greater than 4, {5, 6, 7, 8}C: 1 or 2, {1, 2}a. Find P(A).b. Find
a. Use a computer (or random-number table) to generate a random sample of 56 M&M’s, using the corresponding theoretical probabilities for each color.b. Form a frequency distribution of the random data.c. Construct a bar graph showing the relative frequencies for each color. Use the same color
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.
A woman and a man (unrelated) each have 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
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. What
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
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
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?
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 will wake 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
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 outcomeb. P(both show heads)c. P(exactly one head shows)d. P(neither coin shows a head)e. P(both show
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?FYI Draw a tree diagram.
Salespersons Adams and Jones call on three and four customers, respectively, on a given day.Adams could make 0, 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
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?
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
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, then
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.Opinion Employee Favor Neutral Opposed Total Male 800 200 500 1500 Female 400 100 500 1000
As listed in The World Factbook, 2004, the age structure of the U.S. population is as follows.Male Female 0–14 years 31,122,974 29,713,748 15–64 years 97,756,380 98,183,309 65 years and over 15,078,204 21,172,956 Source: The World Factbook, January 2004,
Suppose a certain ophthalmic trait is associated with eye color. Three hundred randomly selected individuals are studied, with results given in the following table.Eye Color Trait Blue Brown Other Total Yes 70 30 20 120 No 20 110 50 180 Total 90 140 70 300a. What is the probability that a person
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
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
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
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 the plane lands on time.
Suppose that when a job candidate comes to interview 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 wants the candidate (B) is 0.36. The probability P(A B) is 0.88.a. Find P(A and B).b. Find P(B
A traffic analysis at a busy traffic circle in Washington, DC, showed that 0.8 of the autos using the circle entered from Connecticut Avenue. Of those entering the traffic circle from Connecticut Avenue, 0.7 continued on Connecticut Avenue at the opposite side of the circle. What is the probability
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 is
Explain why these probabilities cannot be legitimate: P(A) 0.6, P(B) 0.4, P(A and B) 0.7.
Show that if event A is a subset of event B, then P(A or B) P(B).
The age and gender demographics for the 2004 Monroe Community College students are outlined in the following table.19 and Younger 20–24 25–29 30 and Older Female 3136 2736 1067 2648 Male 2877 2757 779 1502 Total 6013 5493 1846 4150 If one of these students is selected at random, what is the
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).Rural Suburban Urban Total 1–7 Days 90
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

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