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

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 American Pet Products Association’s 2007–2008 National Pet Owners Survey, the following statistics were reported. Number of Pet Dogs
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
As reported in the chapter opener “USA and Its Automobiles,” Americans are in love with the automobile—the majority have more than one vehicle per household. In fact, the national average is 2.28 vehicles per household. The number of vehicles per household in the United States can be
The random variable A has the following probability distribution:a. Find the mean and standard deviation of a. b. How much of the probability distribution is within 2 standard deviations of the mean? c. What is the probability that A is between µ _ 2Ïƒ and m _ 2 Ïƒ?
The random variable has the following probability distribution:a. Find the mean and standard deviation of b. What is the probability that is between m _ Ïƒ and m _ s ?
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 and
Simulates playing a game where a player has a 0.2 probability of winning $3 and a 0.8 probability of losing $1.Repeat the simulations for several sets of 100 plays using the “Play 25 times” button. a. What would you estimate for your expected value (average gain or loss) from the results? b.
a. Use a computer (or random number table) to generate a random sample of 25 observations drawn from the following discrete probability distribution.Compare the resulting data to your expectations. b. Form a relative frequency distribution of the random data. c. Construct a probability histogram of
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 – x/10 for x _ 1, 2, 3, 4 List the resulting sample. (Use the computer commands in Exercise 5.36; just change the arguments.) b. Form a relative
Every Tuesday, Jason’s Video has “roll-the-dice” 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
Consider the four-question multiple-choice quiz presented at the beginning of this section 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 246, where did 1/3 and 4 come from? Why multiply them
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.
Identify the properties that make flipping a coin 50 times and keeping track of heads a binomial experiment.
Evaluate each of the following.
Show that each of the following is true for any values of n and k. Use two specific sets of values for n and k to show that each is true.
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.
A die is rolled 20 times, and the number of “fives” that occur is reported as being the random variable. Explain why x is a binomial random variable.
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
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.
Consider a binomial experiment made up of three trials with outcomes of success, S, and failure, F, where P(S) _ p and P(F) = q.a. Complete the accompanying tree diagram. Label all branches completely.b. In column (b) of the tree diagram, express the probability of each outcome represented by the
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.
Draw a tree diagram picturing a binomial experiment of four trials.
Use the probability function for three coin tosses as demonstrated on page 239 and verify the probabilities for x _ 0, 2 and 3.
a. The probability that all 20 will surviveb. The probability that at most 16 survivec. The probability that at least 18 survive
Demonstrates calculating a binomial probability along with a visual interpretation. Suppose that you are in a class of 30 students and it is assumed that approximately11% of the population is left-handed. Inputting and p _ 0.11 compute the following: a. The probability that exactly five students
If x is a binomial random variable, calculate the probability of x for each case.
If x is a binomial random variable, use Table 2 in Appendix B to determine the probability of x for each of the following: a. n _ 10, x _ 8, p _ 0.3 b. n _ 8, x _ 7, p _ 0.95 c. n _ 15, x _ 3, p _ 0.05 d. n _ 12, x _ 12, p _ 0.99 e. n _ 9, x _ 0, p _ 0.5 f. n _ 6, x _ 1, p _ 0.01 g. Explain the
Test the following function to determine whether or not it is a binomial probability function. List the distribution of probabilities and sketch a histogram.
According to a National Safety Council report, up to 78% of automobile collisions are a result of distractions such as text messaging, phoning a pal, or fumbling with the stereo. Consider a randomly selected group of 18 reported collisions. a. What is the probability that all of the collisions will
A social worker is involved in a study about family structure. She obtains information regarding the number of children per family in 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.
According to the article “Season’s Cleaning,” the U.S. Department of Energy reports that 25% of people with two-car garages don’t have room to park any cars inside. Assuming this to be true, what is the probability of the following? a. Exactly 3 two-car-garage households of a random sample
Can playing video games as a child and teenager lead to a gambling or substance addiction? According to the April 11, 2009, USA Today article “Kids show addiction symptoms,” research published in the Journal Psychological Science found that 8.5% of video-game playing children and teens
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.
As a quality-control inspector of 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, what is the probability that a randomly selected toy truck has no off-center wheels?
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?
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.)
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 May 26, 2009, USA Today Snapshot “Overcoming identity theft” reported the results from a poll of identity-theft victims. According to the source, Affinion Security Center, 20% of the victims stated that it took “one week to one month” to recover from identity theft. A group of 14
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. a. What is the probability that none of the 10 has any body
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?
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.)
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.)
Find the mean and standard deviation for the binomial random variable x with n _ 30 and p _ 0.6 using formulas (5.7) and (5.8).
Consider the binomial distribution where n _ 11 and p _ 0.05. a. Find the mean and standard deviation using formulas (5.7) and (5.8). b. Using Table 2 in Appendix B, list the probability distribution and draw a histogram. c. Locate m and s on the histogram.
Consider the binomial distribution where n _ 11 and p _ 0.05 (see Exercise 5.74) a. Use the distribution [Exercise 5.74(b) or Table 2] and find the mean and standard deviation using formulas (5.1), (5.3a), and (5.4). b. Compare the results of part a with the answers found in Exercise 5.74(a).
a. Calculate the mean and standard deviation of the random variable by using formulas (5.1), (5.3a), and (5.4).b. Calculate the mean and standard deviation using formulas (5.7) and (5.8).c. Compare the results of parts a and b.
Find the mean and standard deviation of x for each of the following binomial random variables: a. The number of tails seen in 50 tosses of a quarter b. The number of left-handed students in a classroom of 40 students (Assume that 11% of the population is left-handed.) c. The number of cars found to
Find the mean and standard deviation for each of the following binomial random variables in parts a–c: a. The number of sixes seen in 50 rolls of a die b. The number of defective televisions in a shipment of 125 (The manufacturer claimed that 98% of the sets were operative.) c. The number of
According to United Mileage Plus Visa (November 22, 2004), 41% of passengers say they “put on the earphones” to avoid being bothered by their seatmates during flights. To show how important, or not important, the earphones are to people, consider the variable x to be the number of people in a
According to the USA Today 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.
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 0 B(12, 0.30)) b. Use Table 5.8 to verify the answer in part a.
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
Use a computer to find the probabilities for all possible x values for a binomial experiment where n _ 30 and p _ 0.35.
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.
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
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 Today Snapshot on January 18, 2005, with 40% of the respondents saying they “open the windows” to fight off sleep. Suppose that 35 U.S.
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 payments and the bank forecloses. Source: www.ricedelman.com Given that 20
The increase in Internet usage over the past few years has been phenomenal, as demonstrated by the February 2004 report from the 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
A binomial random variable has a mean equal to 200 and a standard deviation of 10. Find the values of n and p.
The probability of success on a single trial of a binomial experiment is known to be .The random variable x, number of successes, has a mean value of 80. Find the number of trials involved in this experiment and the standard deviation of x.
A binomial random variable x is based on 15 trials with the probability of success equal to 0.4. Find the probability that this variable will take on a value more than 2 standard deviations above the mean.
A binomial random variable x is based on 15 trials with the probability of success equal to 0.2. Find the probability that this variable will take on a value more than 2 standard deviations from the mean.
a. When using the exact binomial test 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 larger than 0.05? c. An employer has
Extended to overtime in 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
Imprints Galore buys T-shirts (to be imprinted with an item of the customer’s choice) from a manufacturer who guarantees that the shirts have been inspected and that no more than 1% are imperfect in any way. The shirts arrive in boxes of 12. Let x be the number of imperfect shirts found in any
Did you ever buy an incandescent light bulb that failed (either burned out or did not work) the first time you turned the light switch on? When you put a new bulb into a light fixture, you expect it to light, and most of the time it does. Consider 8-packs of 60-watt bulbs and let x be the number of
a. Explain the difference and the relationship between a probability distribution and a probability function. b. Explain the difference and the relationship between a probability distribution and a frequency distribution, and explain how they relate to a population and a sample.
Verify whether or not each of the following is a probability function. State your conclusion and explain.
a. Explain why the IQ score is a continuous variable. b. What are the mean and the standard deviation for the distribution of: IQ scores? SAT scores? standard scores? c. Express, algebraically or as an equation, the relationship between standard scores and IQ scores and the relationship between
According to a September 2008 poll and report done by Pew/Internet, 62% of employed adults use the Internet or e-mail on their jobs. What is the probability that more than 180 out of 250 employed adults use the Internet or e-mail on their jobs?
According to Federal Highway Administration 2007 statistics, the percent of licensed female drivers has just surpassed the percent of licensed male drivers. Of the drivers in the United States, 50.2% are females. If a random sample of 50 drivers is to be selected for a survey, a. what is the
According to a November 2008 survey completed by the Pew Internet & American Life Project [www. pewinternet.org], about 74% of all adult Internet users say they went online for news and information about the 2008 election or to communicate with others about the election race. Assuming the
Not all NBA coaches who enjoy lengthy careers consistently put together winning seasons with the teams they coach. For example, Bill Fitch, who coached 25 seasons of professional basketball after starting his coaching career at the University of Minnesota, won 944 games but lost 1106 while working
Eighty-eight percent of voters would vote for a female presidential candidate if she was qualified, a poll found. The poll was conducted in February 2007 by Gallup and reported by the Pew Research Center [pewresearch.org]. Only 53% of voters felt this way in 1969. Assuming 88% is the true current
According to a December 2008 report from the Join Together website of the Boston University School of Public Health, approximately half (42%) of U.S. children are exposed to secondhand smoke on a weekly basis, with more than 25% of parents reporting that their child has been exposed to smoke in
You are not alone if your garage is so cluttered that you cannot fit your car inside. According to the Democrat & Chronicle article “Season’s cleaning” (January 1, 2009), the U.S. Department of Energy reports that 25% of people with two-car garages don’t have room to park any cars inside
Technology is the key to our future. Apparently, students believe this also. According to an April 2009 poll of high school students by Ridgid, the top career choice for high school students was information technology, selected by 25% of the surveyed students. Suppose you randomly select 200
According to Chebyshev’s theorem, at least how much area is there under the standard normal distribution between z = -2 and z = +2? What is the actual area under the standard normal distribution between z = -2 and z = +2?
The middle 60% of a normally distributed population lies between what two standard scores?
Find the following areas under the standard normal curve. a. To the right of z = - 0.47 P(z > - 0.47) b. To the right of z = - 1.01 P(z > -1.01) c. To the right of z = - 3.39 P(z > -3.39)
Find the standard score z such that the area above the mean and below z under the normal curve is a. 0.3962. b. 0.4846. c. 0.3712.
Find the standard score z such that the area below the mean and above z under the normal curve is a. 0.3212. b. 0.4788. c. 0.2700.
Given that z is the standard normal variable, find the value of k such that a. .P(|z| > 1.68) = k. b. P(|z| < 2.15) = k.
Given that z is the standard normal variable, find the value of c such that: a. P(|z| > c) = 0.0384. b. P(|z| < c) = 0.8740.
Find the following values of z: a. z(0.12) b. z(0.28) c. z(0.85) d. z(0.99)
Find the area under the normal curve that lies between the following pairs of z-values: a. z = -3.00 and z = 3.00 b. z(0.975) and z(0.025) c. z(o.io) and z(o.oi)
Based on data from ACT in 2008, the average science reasoning test score was 20.8, with a standard deviation of 4.6. Assuming that the scores are normally distributed, a. find the probability that a randomly selected student has a science reasoning ACT score of least 25. b. find the probability
The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.67 inches and a standard deviation of 4.38 inches [Department of Commerce; State, Regional and National Monthly Precipitation Report]. If the annual pre-cipitation amount has a normal
A company that manufactures rivets used by commercial aircraft manufacturers knows that the shearing strength of (force required to break) its rivets is of major concern. They believe the shearing strength of their rivets is normally distributed, with a mean of 925 pounds and a standard deviation
In a study of the length of time it takes to play Major League Baseball games during the early 2008 season, the variable “time of game” appeared to be normally distributed, with a mean of 2 hours 49 minutes and a standard deviation of 2i minutes. Source: mlb.com/ a. Some fans describe a game as
The length of the life of a certain type of refrigerator is approximately normally distributed with a mean of 4.8 years and a standard deviation of 1.3 years. a. If this machine is guaranteed for 2 years, what is the probability that the machine you purchased will require replacement under the
In a large industrial complex, the maintenance department has been instructed to replace light bulbs before they burn out. It is known that the life of light bulbs is normally distributed with a mean life of 900 hours of use and a standard deviation of 75 hours. When should the light bulbs be
A machine is programmed to fill 10-oz containers with a cleanser. However, the variability inherent in any machine causes the actual amounts of fill to vary. The dis-tribution is normal with a standard deviation of 0.02 oz. What must the mean amount m be so that only 5% of the containers receive
The grades on an examination whose mean is 525 and whose standard deviation is 80 are normally distributed. a. Anyone who scores below 350 will be retested. What percentage does this represent? b. The top 12% are to receive a special commendation. What score must be surpassed to receive this
A soft drink vending machine can be regulated so that it dispenses an average of m oz of soft drink per cup. a. If the ounces dispensed per cup are normally distributed with a standard deviation of 0.2 oz, find the setting for m that will allow a 6-oz glass to hold (without overflowing) the amount
Suppose that x has a binomial distribution with n = 25 and p = 0.3. a. Explain why the normal approximation is reasonable. b. Find the mean and standard deviation of the normal distribution that is used in the approximation.
Let x be a binomial random variable for n = 30 and p = 0.1. a. Explain why the normal approximation is not reasonable. b. Find the function used to calculate the probability of any x from x = 0 to x = 30. c. Use a computer or calculator to list the probability distribution.
a. Use a computer or calculator to list the binomial probabilities for the distribution where n = 50 and p = 0.1. b. Use the results from part a to find P(x < 6). c. Find the normal approximation for P(x < 6), and compare the results with those in part b.
a. Use a computer or calculator to list both the probability distribution and the cumulative probability distribution for the binomial probability experiment with n = 40 and p = 0.4. b. Explain the relationship between the two distributions found in part a. c. If you could use only one of these

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