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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions
The digital video recorder (DVR) is a common fixture in most American households. In fact, most American households have DVRs, and many have more than one. A sample of 25 households produced the following measurements on x, the number of DVRs in the household:a. Is the distribution of x, the number
The set of presidential vetoes in Exercise 1.47 and data set EX0147 is listed here, along with a box plot generated by MINITAB. Use the box plot to describe the shape of the distribution and identify any outliers.
Altman and Bland report the survival times for patients with active hepatitis, half treated with prednisone and half receiving no treatment. The survival times (in months) (Exercise 1.25 and EX0125) are adapted from their data for those treated with prednisone.a. Can you tell by looking at the data
The monthly utility bills for a household in Riverside, California, were recorded for 12 consecutive months starting in January 2010:a. Construct a box plot for the monthly utility costs.b. What does the box plot tell you about the distribution of utility costs for this household?
The number of raisins in each of 14 mini boxes (1/2-ounce size) was counted for a generic brand and for Sun maid brand raisins. The two data sets are shown here:a. What are the mean and standard deviation for the generic brand?b. What are the mean and standard deviation for the Sun maid brand?c.
The number of raisins in each of 14 miniboxes (1/2-ounce size) was counted for a generic brand and for Sun maid brand raisins. The two data sets are shown here:For Information: Refer to Exercise 2.54.a. Find the median, the upper and lower quartiles, and the IQR for each of the two data sets.b.
The number of television viewing hours per household and the prime viewing times are two factors that affect television advertising income. A random sample of 25 households in a particular viewing area produced the following estimates of viewing hours per household:a. Scan the data and use the
Refer to Exercise 1.26 and data set EX0126. The lengths of time (in months) between the onset of a particular illness and its recurrence were recorded:Exercise 1.26 The length of time (in months) between the onset of a particular illness and its recurrence was recorded for n = 50 patients: a. Find
Refer to Exercise 1.26 and data set EX0126. The lengths of time (in months) between the onset of a particular illness and its recurrence were recorded:The length of time (in months) between the onset of a particular illness and its recurrence was recorded for n = 50 patients: a. Examine the data
Find the median and the lower and upper quartiles for the data on times until recurrence of an illness in Exercise 2.57. Use these descriptive measures to construct a box plot for the data. Use the box plot to describe the data distribution.Exercise 2.57.Refer to Exercise 1.26 and data set EX0126.
Ten of the 50 largest businesses in the United States, randomly selected from the Fortune 500, are listed below along with their revenues (in millions of dollars):a. Draw a stem and leaf plot for the data. Are the data skewed?b. Calculate the mean revenue for these 10 businesses. Calculate the
Refer to Exercise 2.8. The prices of a 6-ounce can or a 7.06-ounce pouch for 14 different brands of water-packed light tuna, based on prices paid nationally in supermarkets, are reproduced here.a. Calculate the five-number summary.b. Construct a box plot for the data. Are there any outliers?c. The
An analytical chemist wanted to use electrolysis to determine the number of moles of cupric ions in a given volume of solution. The solution was partitioned into n = 30 portions of .2 milliliter each, and each of the portions was tested. The average number of moles of cupric ions for the n = 30
According to the EPA, chloroform, which in its gaseous form is suspected of being a cancer-causing agent, is present in small quantities in all of the country's 240,000 public water sources. If the mean and standard deviation of the amounts of chloroform present in the water sources are 34 and 53
Mathematics achievement test scores for 400 students were found to have a mean and a variance equal to 600 and 4900, respectively. If the distribution of test scores was mound-shaped, approximately how many of the scores would fall into the interval 530 to 670? Approximately how many scores would
How much sleep do you get on a typical school night? A group of 10 college students were asked to report the number of hours that they slept on the previous night with the following results:a. Find the mean and the standard deviation of the number of hours of sleep for these 10 students.b.
The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March follow.a. What are the maximum and minimum miles per gallon? What is the range?b. Construct a relative frequency histogram for these data. How would you describe the shape of the
Refer to Exercise 2.65. Construct a box plot for the data. Are there any outliers? Does this conclusion agree with your results in Exercise 2.65?Exercise 2.65The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March follow.
Petroleum pollution in seas and oceans stimulates the growth of some types of bacteria. A count of petroleumlytic micro-organisms (bacteria per 100 milliliters) in 10 portions of seawater gave these readings:a. Guess the value for s using the range approximation. b. Calculate and s and compare
Attendances at a high school's basketball games were recorded and found to have a sample mean and variance of 420 and 25, respectively. Calculate ± s, ± 2s, and ± 3s. and then state the approximate fractions of measurements you would expect to fall into these intervals according to the
The College Board's verbal and mathematics scholastic aptitude tests are scored on a scale of 200 to 800. It seems reasonable to assume that a distribution of all test scores, either verbal or math, is mound-shaped. If σ is the standard deviation of one of these distributions, what is the largest
Does birth order have any effect on a person's personality? A report on a study by an MIT researcher indicates that later-born children are more likely to challenge the establishment, more open to new ideas, and more accepting of change. In fact, the number of later born children is increasing.
A strain of long-stemmed roses has an approximate normal distribution with a mean stem length of 15 inches and standard deviation of 2.5 inches. a. If one accepts as "long-stemmed roses" only those roses with a stem length greater than 12.5 inches, what percentage of such roses would be
A pharmaceutical company wishes to know whether an experimental drug being tested in its laboratories has any effect on systolic blood pressure. Fifteen randomly selected subjects were given the drug, and their systolic blood pressures (in millimeters) are recorded.a. Guess the value of s using the
A company interested in lumbering rights for a certain tract of slash pine trees is told that the mean diameter of these trees is 14 inches with a standard deviation of 2.8 inches.Assume the distribution of diameters is roughly mound-shaped.a. What fraction of the trees will have diameters between
The following data represent the social ambivalence scores for 15 people as measured by a psychological test. (The higher the score, the stronger the ambivalence.)a. Guess the value of s using the range approximation. b. Calculate and s for the 15 social ambivalence scores. c. What fraction of the
The mean duration of television commercials on a given network is 75 seconds, with a standard deviation of 20 seconds. Assume that durations are approximately normally distributed. a. What is the approximate probability that a commercial will last less than 35 seconds? b. What is the approximate
A random sample of 100 foxes was examined by a team of veterinarians to determine the prevalence of a particular type of parasite. Counting the number of parasites per fox, the veterinarians found that 69 foxes had no parasites, 17 had one parasite, and so on. A frequency tabulation of the data is
Consider a population consisting of the number of teachers per college at small 2-year colleges. Suppose that the number of teachers per college has an average µ = 175 and a standard deviation σ = 15. a. Use Tchebysheff's Theorem to make a statement about the percentage of colleges that have
From the following data, a student calculated s to be .263. On what grounds might we doubt his accuracy? What is the correct value (to the nearest hundredth)?
In the summer of 2001, Barry Bonds began his quest to break Mark McGwire's record of 70 home runs hit in a single season. At the end of the 2003 major league baseball season, the number of home runs hit per season by each of four major league superstars over each player's career were recorded, and
An article in Consumer Reports gives the price-an estimated average for a 6-ounce can or a 7.06-ounce pouch-for 14 different brands of water-packed light tuna, based on prices paid nationally in supermarkets:a. Find the average price for the 14 different brands of tuna.b. Find the median price for
In the seasons that followed his 2001 record-breaking season, Barry Bonds hit 46, 45, 45, 5, 26, and 28 homers, respectively, until he retired from major league baseball in 2007 (www.ESPN.com). Two box plots, one of Bond's homers through 2001, and a second including the years 2002-2007 follow.The
Here are the ages of 50 pennies from Exercise 1.45 and data set EX0145. The data have been sorted from smallest to largest.Exercise 1.45 Construct a box plot for these data and identify any outliers: a. What is the average age of the pennies? b. What is the median age of the pennies? c. Based on
Here are a few facts reported as Snapshots in USA Today. • About 12% of America's volunteers spend more than 5 hours per week volunteering. • Fifty-eight percent of all cars in operation are at least 8 years old. • Twenty-two percent of all fans are willing to pay $75 or more for a ticket to
The following data are the response times in seconds for n = 25 first graders to arrange three objects by size.a. Find the mean and the standard deviation for these 25 response times.b. Order the data from smallest to largest.c. Find the z-scores for the smallest and largest response times. Is
Refer to Exercise 2.84.Exercise 2.84The following data are the response times in seconds for n = 25 first graders to arrange three objects by size.a. Find the five-number summary for this data set.b. Construct a box plot for the data.c. Are there any unusually large or small response times
As professional sports teams become a more and more lucrative business for their owners, the salaries paid to the players have also increased. In fact, sports superstars are paid astronomical salaries for their talents. If you were asked by a sports management firm to describe the distribution of
Which baseball league has had the best hitters? Many of us have heard of baseball greats like Stan Musial, Hank Aaron, Roberto Clemente, and Pete Rose of the National League and Ty Cobb, Babe Ruth, Ted Williams, Rod Carew, and Wade Boggs of the American League. But have you ever heard of Willie
Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers to the first question:a. Create side-by-side pie charts to describe these data.b. Create a side-by-side bar chart to describe these data.c. Draw a stacked bar chart
Consider this set of bivariate data: (1, 6), (3, 2), and (2, 4).a. Calculate the covariance sxy.b. Calculate the correlation coefficient r.c. Calculate the equation of the regression line using the computing formulas.d. Plot the three points and the straight line on a scatterplot. Does the line
A set of bivariate data consists of these measurements on two variables, x and y:a. Draw a scatterplot to describe the data.b. Does there appear to be a relationship between x and y? If so, how do you describe it?c. Calculate the correlation coefficient, r, using the computing formula given in this
Consider this set of bivariate data:a. Draw a scatterplot to describe the data. b. Does there appear to be a relationship between x and y? If so, how do you describe it? c. Calculate the correlation coefficient, r. Does the value of r confirm your conclusions in part b? Explain.
The value of a quantitative variable is measured once a year for a 10-year period:a. Draw a scatterplot to describe the variable as it changes over time. b. Describe the measurements using the graph constructed in part a. c. Use this MINITAB output to calculate the correlation coefficient, r: d.
These data relating the amount spent on groceries per week and the number of household members are from Example 3.3:a. Find the best-fitting line for these data. b. Plot the points and the best-fitting line on the same graph. Does the line summarize the information in the data points? c. What would
The data relating the square feet of living space and the selling price of 12 residential properties given in Example 3.5 are reproduced here. First, find the best-fitting line that describes these data, and then plot the line and the data points on the same graph. Comment on the goodness of the
A social skills training program, reported in Psychology in the Schools, was implemented for seven students with mild handicaps in a study to determine whether the program caused improvement in pre/post measures and behavior ratings. For one such test, these are the pretest and posttest scores for
Male crickets chirp by rubbing their front wings together, and their chirping is temperature dependent. Crickets chirp faster with increasing temperature and slower with decreasing temperatures. The table below shows the number of chirps per second for a cricket, recorded at 10 different
As technology improves, your choice of televisions becomes more complicated. Should you choose an LCD TV, a plasma TV, and with rear or front projection? In the table below, Consumer Reports gives the prices and screen sizes for the top 10 LCD TVs in the 46-inch and higher categories. Does the
A group of items are categorized according to a certain attribute-X, Y, Z-and according to the state in which they are produced:a. Create a comparative (side-by-side) bar chart to compare the numbers of items of each type made in California and New York. b. Create a stacked bar chart to compare the
As technology improves, your choice of televisions becomes more complicated. Should you choose an LCD TV, a plasma TV, and with rear or front projection? In the table below, Consumer Reports gives the prices and screen sizes for the top 10 LCD TVs in the 46-inch and higher categories. Does the
Professor Isaac Asimov was one of the most prolific writers of all time. He wrote nearly 500 books during a 40-year career prior to his death in 1992. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. These data
Health-conscious Americans often consult the nutritional information on food packages in an attempt to avoid foods with large amounts of fat, sodium, or cholesterol. The following information was taken from eight different brands of American cheese slices:a. Which pairs of variables do you expect
In Exercise 1.14, we looked at the age distribution of users of the social networking site Face book (in thousands) as it changed from January 2009 to January 2010. The online article also provided insight into other demographics of Face book users during this time period.9 Two bar charts,
The demand for healthy foods that are low in fats and calories has resulted in a large number of "low-fat" and "fat-free" products at the supermarket. The table shows the numbers of calories and the amounts of sodium (in milligrams) per slice for five different brands of fat-free American cheese.a.
Using a chemical procedure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given amount of nickel (in parts per billion) is added to a buffer. The data are shown here:Use a graph to describe the relationship
How much money do movies make on a single weekend? Does this amount in any way predict the movie's success or failure, or is the movie's total monetary success more dependent on the number of weeks that the movie remains in the movie theaters? In a recent week, the following data was collected for
The data from Exercise 3.26 were entered into a MINITAB worksheet, and the following output was obtained.Exercise 3.26 How much money do movies make on a single weekend? Does this amount in any way predict the movie's success or failure, or is the movie's total monetary success more dependent on
Refer to Exercise 1.54 and data set EX0154. When the heights of these 105 students were recorded, their gender was also recorded.Exercise 1.54The self-reported heights of 105 students in a biostatistics class are described in the relative frequency histogram below.a. What variables have been
The data in Exercise 1.37 gave the number of hazardous waste sites in each of the 50 states and the District of Columbia in 2009. Suspecting that there might be a relationship between the number of waste sites and the size of the state (in thousands of square miles), researchers recorded both
The table below shows the average amounts spent per week by men and women in each of four spending categories:a. What possible graphical methods could you use to compare the spending patterns of women and men? b. Choose two different methods of graphing and display the data in graphical form. c.
The number of passes completed and the total number of passing yards were recorded for Aaron Rodgers for each of the 15 regular season games that he played in the fall of 2010:a. Draw a scatterplot to describe the relationship between number of completions and total passing yards for Aaron
In Exercise 1.59, we analyzed the percentage of aluminum oxide in 26 samples of Romano-British pottery found at four different kiln sites in the United Kingdom.13 Since one of the sites only provided two measurements, that site is eliminated, and comparative box plots of aluminum oxide at the other
Here is the percentage of aluminum oxide, the percentage of iron oxide, and the percentage of magnesium oxide in five samples collected at Ashley Rails in the United Kingdom.a. Find the correlation coefficients describing the relationships between aluminum and iron oxide content, between iron oxide
The table below shows the gestation time in days and the average longevity in years for a variety of mammals in captivity; the potential life span of animals is rarely attained for animals in the wild.a. Draw a scatterplot for the data. b. Describe the form, direction, and strength for the pattern
As the United States fell further and further into a recession in the years 2007-2009, the number of families who had to default on their mortgages and those who actually lost their homes grew. However, as we recover from the recession, Moody's Economy predicts that these numbers will fall.14 The
Leonardo da Vinci (1452-1519) drew a sketch of a man, indicating that a person's armspan (measuring across the back with arms outstretched to make a "T") is roughly equal to the person's height. To test this claim, we measured eight people with the following results:a. Draw a scatterplot for
When a student performs poorly on a midterm exam, the student sometimes is convinced that their score is an anomaly and that they will do much better on the second midterm. The data below show the midterm scores (out of 100 points) for eight students in an introductory statistics class.a. Construct
When a student performs poorly on a midterm exam, the student sometimes is convinced that their score is an anomaly and that they will do much better on the second midterm. The data below show the midterm scores (out of 100 points) for eight students in an introductory statistics class.For
Of two personnel evaluation techniques available, the first requires a 2-hour test-interview while the second can be completed in less than an hour. The scores for each of the eight individuals who took both tests are given in the next table.a. Construct a scatterplot for the data. b. Describe the
Of two personnel evaluation techniques available, the first requires a 2-hour test-interview while the second can be completed in less than an hour. The scores for each of the eight individuals who took both tests are given in the next table.a. Find the correlation coefficient, r, to describe the
The color distributions for two snack-size bags of M&M'S® candies, one plain and one peanut, are displayed in the table. Choose an appropriate graphical method and compare the distributions.
Is there a correlation between the amount of rain and the amount of snow that falls in a particular location? The table below shows the average annual rainfall (inches) and the average annual snowfall (inches) for 10 cities in the United States.a. Construct a scatterplot for the data. b. Calculate
The table below shows the prices of nine Verizon smart-phones along with their overall score (on a scale of 0-100) in a consumer rating survey presented by Consumer Reports.a. Plot the nine data points using a scatterplot.Describe the form, direction, and strength of the relationship between price
When you were growing up, did you feel that you did not have enough free time? Parents and children have differing opinions on this subject. A research group surveyed 198 parents and 200 children and recorded their responses to the question, "How much free time does your child have?" or "How much
The price of living in the United States has increased dramatically in the past decade, as demonstrated by the consumer price indexes (CPIs) for housing and transportation. These CPIs are listed in the table for the years 1996 through the first half of 2010.a. Create side-by-side comparative bar
A local chamber of commerce surveyed 126 households within its city and recorded the type of residence and the number of family members in each of the households. The data are shown in the table.a. Use a side-by-side bar chart to compare the number of family members living in each of the three
Not only is the Face book social networking site growing rapidly in the United States, but the composition of Face book members depends on both age and gender. During a 1-month period in early 2010, Face book reported its growth by both age and gender, as shown in the table.a. Construct a stacked
Suppose that the relationship between two variables x and y can be described by the regression line y = 2.0 + 0.5x. a. What is the change in y for a one-unit change in x? b. Do the values of y increase or decrease as x increases? c. At what point does the line cross the y-axis? What is the name
Does the price of an appliance convey something about its quality? Forty-eight different dishwashers were ranked on characteristics ranging from an overall satisfaction score, washing (x1), energy use (x2), noise (x3), ease of use (x4), and cycle time (in minutes). The Bosch (SHE55M1[2]UC) had the
An experiment involves tossing a single die. These are some events: A: Observe a 2 B: Observe an even number C: Observe a number greater than 2 D: Observe both A and B E: Observe A or B or both F: Observe both A and C a. List the simple events in the sample space. b. List the simple events in each
The game of roulette uses a wheel containing 38 pockets. Thirty-six pockets are numbered 1, 2, . . . , 36, and the remaining two are marked 0 and 00. The wheel is spun, and a pocket is identified as the "winner." Assume that the observance of any one pocket is just as likely as any other. a.
A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability of winning?
Although there is legal protection for "whistle blowers"-employees who report illegal or unethical activities in the workplace-it has been reported that approximately 23% of those who reported fraud suffered reprisals such as demotion or poor performance ratings. Suppose the probability that an
Two cold tablets are unintentionally placed in a box containing two aspirin tablets. The four tablets are identical in appearance. One tablet is selected at random from the box and is swallowed by the first patient. A tablet is then selected at random from the three remaining tablets and is
Refer to Exercise 4.102. By summing the probabilities of simple events, find P(A), P(B), P(A ∩ B), P(A ∪ B), P(C), P(A ∩ C), and P(A ∪ C). Exercise 4.102 Two cold tablets are unintentionally placed in a box containing two aspirin tablets. The four tablets are identical in appearance. One
A retailer sells two styles of high-priced digital video recorders (DVR) that experience indicates are in equal demand. (Fifty percent of all potential customers prefer style 1, and 50% favor style 2.) If the retailer stocks four of each, what is the probability that the first four customers
A shipping container contains seven complex electronic systems. Unknown to the purchaser, three are defective. Two of the seven are selected for thorough testing and are then classified as defective or nondefective. What is the probability that no defectives are found?
A heavy-equipment salesman can contact either one or two customers per day with probabilities 1/3 and 2/3, respectively. Each contact will result in either no sale or a $50,000 sale with probabilities 9/10 and 1/10, respectively. What is the expected value of his daily sales?
A county containing a large number of rural homes is thought to have 60% of those homes insured against fire. Four rural homeowners are chosen at random from the entire population, and x are found to be insured against fire. Find the probability distribution for x. What is the probability that at
A fire-detection device uses three temperature-sensitive cells acting independently of one another in such a manner that any one or more can activate the alarm. Each cell has a probability p = .8 of activating the alarm when the temperature reaches 135°F or higher. Let x equal the number of cells
Exercise 4.10 described the game of roulette. Suppose you bet $5 on a single number-say, the number 18. The payoff on this type of bet is usually 35 to 1. What is your expected gain?
Three people are randomly selected to report for jury duty. The gender of each person is noted by the county clerk. a. Define the experiment. b. List the simple events in S. c. If each person is just as likely to be a man as a woman, what probability do you assign to each simple event? d. What is
Refer to the experiment conducted by Gregor Mendel in Exercise 4.64. Suppose you are interested in following two independent traits in snap peas-seed texture (S = smooth, s = wrinkled) and seed color (Y = yellow, y = green)-in a second-generation cross of heterozygous parents. Remember that the
An investor has the option of investing in three of five recommended stocks. Unknown to her, only two will show a substantial profit within the next 5 years. If she selects the three stocks at random (giving every combination of three stocks an equal chance of selection), what is the probability
Four union men, two from a minority group, are assigned to four distinctly different one-man jobs, which can be ranked in order of desirability. a. Define the experiment. b. List the simple events in S. c. If the assignment to the jobs is unbiased-that is, if any one ordering of assignments is as
A salesperson figures that the probability of her making a sale during the first contact with a client is .4 but improves to .55 on the second contact if the client did not buy during the first contact. Suppose this salesperson makes one and only one callback to any client. If she contacts a
A man takes either a bus or the subway to work with probabilities .3 and .7, respectively. When he takes the bus, he is late 30% of the days. When he takes the subway, he is late 20% of the days. If the man is late for work on a particular day, what is the probability that he took the bus?
The failure rate for a guided missile control system is 1 in 1000. Suppose that a duplicate, but completely independent, control system is installed in each missile so that, if the first fails, the second can take over. The reliability of a missile is the probability that it does not fail. What is
A rental truck agency services its vehicles on a regular basis, routinely checking for mechanical problems. Suppose that the agency has six moving vans, two of which need to have new brakes. During a routine check, the vans are tested one at a time. a. What is the probability that the last van with
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