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mathematics
statistics

Introductory Statistics 8th Edition Prem S. Mann - Solutions

How much does the typical American family spend to go away on vacation each year? Twenty five randomly selected households reported the following vacation expenditures (rounded to the nearest hundred dollars) during the past year:a. Using both graphical and numerical methods, organize and interpret
Actuaries at an insurance company must determine a premium for a new type of insurance. A random sample of 40 potential purchasers of this type of insurance was found to have suffered the following values of losses (in dollars) during the past year. These losses would have been covered by the
A local golf club has men€™s and women€™s summer leagues. The following data give the scores for a round of 18 holes of golf for 17 men and 15 women randomly selected from their respective leagues.a. Make a box-and-whisker plot for each of the data sets and use them to discuss the
Answer the following questions.a. The total weight of all pieces of luggage loaded onto an airplane is 12,372 pounds, which works out to be an average of 51.55 pounds per piece. How many pieces of luggage are on the plane?b. A group of seven friends, having just gotten back a chemistry exam,
Suppose that there are 150 freshmen engineering majors at a college and each of them will take the same five courses next semester. Four of these courses will be taught in small sections of 25 students each, whereas the fifth course will be taught in one section containing all 150 freshmen. To
The following data give the 2010 revenues (in millions of dollars) of the six Maryland-based companies listed in the 2010 Fortune 500 (www.money.cnn.com/magazines/fortune/fortune500/2010/states/MD.html). The data refer to the following companies, respectively: Lockheed Martin, Constellation Energy,
The following data give the weights (in pounds) of a random sample of 44 college students. (Here F and M indicate female and male, respectively.)Compute the mean, median, and standard deviation for the weights of all students, of men only, and of women only. Of the mean and median, which is the
The distribution of the lengths of fish in a certain lake is not known, but it is definitely not bell shaped. It is estimated that the mean length is 6 inches with a standard deviation of 2 inches.a. At least what proportions of fish in the lake are between 3 inches and 9 inches long?b. What is the
The following stem-and-leaf diagram gives the distances (in thousands of miles) driven during the past year by a sample of drivers in a city.a. Compute the sample mean, median, and mode for the data on distances driven. b. Compute the range, variance, and standard deviation for these data. c.
Refer to the data in Problem 3.140. Two individuals, one from Canada and one from England, are interested in your analysis of these data but they need your results in different units. The Canadian individual wants the results in grams (1 pound 435.59 grams), while the English individual wants the
Although the standard workweek is 40 hours a week, many people work a lot more than 40 hoursa week. The following data give the numbers of hours worked last week by 50 people.a. The sample mean and sample standard deviation for this data set are 49.012 and 5.080, respectively. Using
Refer to the women€™s golf scores in Exercise 3.137. It turns out that 117 were mistakenly entered. Although this person still had the highest score among the 15 women, her score was not a mild or extreme outlier according to the box-and-whisker plot, nor was she tied for the highest
The following table lists the 2009 total profits (rounded to millions of dollars) of the seven Fortune 500 companies in the Computers, Office Equipment category (Source: www.money.cnn.com/magazines/ fortune/fortune500/2010/industries/8/index.html). 2009 Profit Company (millions of
The following data give the numbers of car thefts that occurred in a city during the past 12 days.Find the mean, median, and mode.
The following data give the amount of money (in dollars) that each of six Canadian social service charities spent to raise $100 in donations during 2010 (www.moneysense.ca). The values, listed in that order, are for the Calgary Inter-Faith Food Bank Society, Covenant House Toronto, The Salvation
The following table gives the number of major penalties for each of the 15 teams in the Eastern Conference of the National Hockey League during the 2010–11 seasons (www.nhl.com). A major penalty is subject to 5 minutes in the penalty box for a player. Number of Team Major
Due to antiquated equipment and frequent windstorms, the town of Oak City often suffers power outages. The following data give the numbers of power outages for each of the past 12 months.Compute the mean, median, and mode for these data.
Briefly explain the meaning of an outlier. Is the mean or the median a better measure of central tendency for a data set that contains outliers? Illustrate with the help of an example.
Standard milk chocolate M&„¢ come in six colors. The Fun Size bags typically contain between 16 and 20 candies, so it is common for a Fun Size bag to have some of the six colors missing. Each of the 14 students in a summer statistics class was given a Fun Size bag and asked to count the
Nixon Corporation manufactures computer monitors. The following data are the numbers of computer monitors produced at the company for a sample of 10 days.Calculate the mean, median, and mode for these data.
Grand Jury indictment data for Gloucester County, New Jersey, are published every week in the Gloucester County Times newspaper (www.nj.com/gloucester). The following data are the number of indictments for a sample of 11 weeks selected from July 2010 through June 2011:Find the mean, median, and
The following data represent the numbers of tornadoes that touched down during 1950 to 1994 in the 12 states that had the most tornadoes during this period. The data for these states are given in the following order: CO, FL, IA, IL, KS, LA, MO, MS, NE, OK, SD, TX.a. Calculate the mean and median
The following data set lists the number of women from each of 12 countries who were on the Rolex Women€™s World Golf Rankings Top 50 list as of July 18, 2011. The data, listed in that order, are for the following countries: Australia, Chinese Taipei, England, Germany, Japan, Netherlands,
One property of the mean is that if we know the means and sample sizes of two (or more) data sets, we can calculate the combined mean of both (or all) data sets. The combined mean for two data sets is calculated by using the formulaWhere n1 and n2 are the sample sizes of the two data sets and 1 and
Twenty business majors and 18 economics majors go bowling. Each student bowls one game. The scorekeeper announces that the mean score for the 18 economics majors is 144 and the mean score for the entire group of 38 students is 150. Find the mean score for the 20 business majors.
For any data, the sum of all values is equal to the product of the sample size and mean; that is, ∑x = n. Suppose the average amount of money spent on shopping by 10 persons during a given week is $105.50. Find the total amount of money spent on shopping by these 10 persons.
The mean 2011 income for five families was $99,520. What was the total 2011 income of these five families?
The mean age of six persons is 46 years. The ages of five of these six persons are 57, 39, 44, 51, and 37 years, respectively. Find the age of the sixth person.
Using an example, show how outliers can affect the value of the mean.
Seven airline passengers in economy class on the same flight paid an average of $361 per ticket. Because the tickets were purchased at different times and from different sources, the prices varied. The first five passengers paid $420, $210, $333, $695, and $485. The sixth and seventh tickets were
Consider the following two data sets.Notice that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the mean for each of these two data sets. Comment on the relationship between the two means.
Consider the following two data sets.Notice that each value of the second data set is obtained by multiplying the corresponding value of the first data set by 2. Calculate the mean for each of these two data sets. Comment on the relationship between the two means.
The trimmed mean is calculated by dropping a certain percentage of values from each end of a ranked data set. The trimmed mean is especially useful as a measure of central tendency when a data set contains a few outliers. Suppose the following data give the ages (in years) of 10 employees of a
The following data give the prices (in thousands of dollars) of 20 houses sold recently in a city.Find the 20% trimmed mean for this data set.
In some applications, certain values in a data set may be considered more important than others. For example, to determine students€™ grades in a course, an instructor may assign a weight to the final exam that is twice as much as that to each of the other exams. In such cases, it is more
When studying phenomena such as inflation or population changes that involve periodic increases or decreases, the geometric mean is used to find the average change over the entire period under study. To calculate the geometric mean of a sequence of n values x1, x2,..., xn, we multiply them together
The range, as a measure of spread, has the disadvantage of being influenced by outliers. Illustrate this with an example.
When is the value of the standard deviation for a data set zero? Give one example. Calculate the standard deviation for the example and show that its value is zero.
Which of the three measures of central tendency (the mean, the median, and the mode) can be calculated for quantitative data only, and which can be calculated for both quantitative and qualitative data? Illustrate with examples.
Briefly explain the difference between a population parameter and a sample statistic. Give one example of each.
The following data set belongs to a population:Calculate the range, variance, and standard deviation.
The following data set belongs to a sample:Calculate the range, variance, and standard deviation.
The following data give the number of shoplifters apprehended during each of the past 8 weeks at a large department store.a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range, variance, and standard
The following data give the prices of seven textbooks randomly selected from a university bookstore.a. Find the mean for these data. Calculate the deviations of the data values from the mean. Is the sum of these deviations zero?b. Calculate the range, variance, and standard deviation.
Refer to Exercise 3.20, which listed the number of colors of M&Ms that each of the 14 Fun Size bags contained. Those data are reproduced here:Calculate the range, variance, and standard deviation.
Refer to the data in Exercise 3.23, which contained the numbers of tornadoes that touched down in 12 states that had the most tornadoes during the period 1950 to 1994. The data are reproduced here.Find the range, variance, and standard deviation for these data.
Refer to Exercise 3.22, which listed the number of indictments handed out by the Gloucester County, New Jersey, Grand Jury during 11 randomly selected weeks from July 2010 to June 2011. The data are reproduced here:Calculate the range, variance, and standard deviation.
The following data give the number of highway collisions with large wild animals, such as deer or moose, in one of the northeastern states during each week of a 9-week period.Find the range, variance, and standard deviation.
Refer to Exercise 3.24, which listed the number of women from each of 12 countries who were on the Rolex Women€™s World Golf Rankings Top 50 list as of July 18, 2011. Those data are reproduced here:Calculate the range, variance, and standard deviation.
The lengths (in seconds) of the eight most recent songs played on 98.9 FM WCLZ and WCLZ.com (Portland, ME) at 1:28 p.m. on Wednesday July 20, 2011 were as follows:Calculate the range, variance, and standard deviation.
Following are the temperatures (in degrees Fahrenheit) observed during eight wintry days in a Midwestern city:Compute the range, variance, and standard deviation.
Refer to Exercise 2.94, which listed the alcohol content by volume for each of the 13 varieties of beer produced by Sierra Nevada Brewery. Those data are reproduced here:Calculate the range, variance, and standard deviation.
The following data represent the total points scored in each of the NFL Super Bowl games played from 2001 through 2012, in that order:Compute the range, variance, and standard deviation for these data.
The following data represent the 2011 guaranteed salaries (in thousands of dollars) of the head coaches of the final eight teams in the 2011 NCAA Men€™s Basketball Championship. The data represent the 2011 salaries of basketball coaches of the following universities, entered in that order:
The following data give the hourly wage rates of eight employees of a company.Calculate the standard deviation. Is its value zero? If yes, why?
The following data are the ages (in years) of six students.Calculate the standard deviation. Is its value zero? If yes, why?
One disadvantage of the standard deviation as a measure of dispersion is that it is a measure of absolute variability and not of relative variability. Sometimes we may need to compare the variability of two different data sets that have different units of measurement. The coefficient of variation
The SAT scores of 100 students have a mean of 975 and a standard deviation of 105. The GPAs of the same 100 students have a mean of 3.16 and a standard deviation of .22. Is the relative variation in SAT scores larger or smaller than that in GPAs?
Consider the following two data sets.Each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. Calculate the standard deviation for each of these two data sets using the formula for sample data. Comment on the relationship between the two standard
Consider the following two data sets.Each value of the second data set is obtained by multiplying the corresponding value of the first data set by 2. Calculate the standard deviation for each of these two data sets using the formula for population data. Comment on the relationship between the two
Are the values of the mean and standard deviation that are calculated using grouped data exact or approximate values of the mean and standard deviation, respectively? Explain.
Using the population formulas, calculate the mean, variance, and standard deviation for the following grouped data.
Using the sample formulas, find the mean, variance, and standard deviation for the grouped data displayed in the following table.
The following table gives the frequency distribution of the amounts of telephone bills for August 2012 for a sample of 50 families.Amount of Telephone Bill (dollars) Number of Families40 to less than 70............ 970 to less than 100........... 11100 to less than 130...........
The following table gives the frequency distribution of the number of hours spent last week on cell phones (making phone calls and texting) by all 100 students of the tenth grade at a school.Hours per Week Number of Students0 to less than 4...........
The following table gives the frequency distribution of the number of hours spent last week on cell phones (making phone calls and texting) by all 100 students of the tenth grade at a school. Hours per Week Number of Students0 to less than
The following table gives the grouped data on the ounces of milk dispensed by a machine into 1 gallon jugs for a sample of 250 jugs of milk selected from a day’s production. Note that 1 gallon is equal to 128 ounces. Ounces of Milk Number of Jugs121 to less than 123......... 5123 to
The following table gives the frequency distribution of the total miles driven during 2012 by 300 car owners. Miles Driven in 2012 (in thousands) Number of Car Owners0 to less than 5............. 75 to less than 10........... 2610 to less than 15............ 5915 to less than
The following table gives information on the amounts (in dollars) of electric bills for August 2012 for a sample of 50 families.Amount of Electric Bill(dollars) Number of Families0 to less than 60............. 560 to less than 120........... 16120 to less than 180........... 11180 to less
For 50 airplanes that arrived late at an airport during a week, the time by which they were late was observed. In the following table, x denotes the time (in minutes) by which an airplane was late, and f denotes the number of airplanes.x f0 to less than 20......... 1 420 to less
Explain the relationships among the mean, median, and mode for symmetric and skewed histograms. Illustrate these relationships with graphs.
The following table gives the frequency distribution of the number of errors committed by a college baseball team in all of the 45 games that it played during the 2011–12 season. Number of Errors Number of Games0.............. 111.............. 142..............
The following table gives the frequency distribution of the number of hours spent per week on activities that involve sports and/or exercise by a sample of 400 Americans. The numbers are consistent with the summary results from the Bureau of Labor Statistics’ American Time Use Survey
Briefly explain Chebyshev’s theorem and its applications.
Briefly explain the empirical rule. To what kind of distribution is it applied?
A sample of 2000 observations has a mean of 74 and a standard deviation of 12. Using Chebyshev’s theorem, find at least what percentage of the observations fall in the intervals x̅ ± 2s, x̅ ± 2.5s, and x̅ ± 3s. Here x̅ ± 2s represents the interval x̅ – 2s to x̅ + 2s, and so on.
A large population has a mean of 230 and a standard deviation of 41. Using Chebyshev’s theorem, find at least what percentage of the observations fall in the intervals µ ± 2σ, µ ± 2.5 σ, and µ ± 3σ
A large population has a bell-shaped distribution with a mean of 310 and a standard deviation of 37. Using the empirical rule, find what percentage of the observations fall in the intervals µ ± 1σ, µ ± 2σ, and µ ± 3σ.
A sample of 3000 observations has a bell-shaped distribution with a mean of 82 and a standard deviation of 16. Using the empirical rule, find what percentage of the observations fall in the intervals ± 1s, ± 2s, and ± 3s.
The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using Chebyshev’s theorem, find at least what percentage of runners who ran this road race completed it ina. 180 to 260 minutesb. 160 to 280 minutesc. 170 to 270 minutes
The 2011 gross sales of all companies in a large city have a mean of $2.3 million and a standard deviation of $.6 million. Using Chebyshev’s theorem, find at least what percentage of companies in this city had 2011 gross sales ofa. $1.1 to $3.5 millionb. $.8 to $3.8 millionc. $.5 to $4.1 million
According to the National Center for Education Statistics (www.nces.ed.gov), the amounts of all loans, including Federal Parent PLUS loans, granted to students during the 2007–2008 academic year had a distribution with a mean of $8109.65. Suppose that the standard deviation of this distribution
The mean monthly mortgage paid by all home owners in a town is $2365 with a standard deviation of $340.a. Using Chebyshev’s theorem, find at least what percentage of all home owners in this town pay a monthly mortgage ofi. $1685 to $3045 ii. $1345 to $3385b. Using Chebyshev’s theorem, find
The mean life of a certain brand of auto batteries is 44 months with a standard deviation of 3 months. Assume that the lives of all auto batteries of this brand have a bell-shaped distribution. Using the empirical rule, find the percentage of auto batteries of this brand that have a life of a. 41
According to the Kaiser Family Foundation, U.S. workers who had employer-provided health insurance paid an average premium of $4129 for family coverage during 2011 (USA TODAY, October 10, 2011). Suppose that the premiums for such family coverage paid this year by all such workers have a bell-shaped
The prices of all college textbooks follow a bell-shaped distribution with a mean of $180 and a standard deviation of $30. a. Using the empirical rule, find the percentage of all college textbooks with their prices between i. $150 and $210 ii. $120 and $240 b. Using the empirical rule, find the
Suppose that on a certain section of I-95 with a posted speed limit of 65 mph, the speeds of all vehicles have a bell-shaped distribution with a mean of 72 mph and a standard deviation of 3 mph. a. Using the empirical rule, find the percentage of vehicles with the following speeds on this section
Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.
Explain how the interquartile range is calculated. Give one example.
Briefly describe how the percentiles are calculated for a data set.
Explain the concept of the percentile rank for an observation of a data set.
The following data set belongs to a population:Calculate the mean, median, and mode.
The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the club.a. Compute the values of the three quartiles and the interquartile range.b. Calculate the (approximate) value of the 82nd percentile.c. Find the percentile rank of 10.
The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84.a. Find the values of the three quartiles and the interquartile range.b. Calculate the (approximate) value of the 35th percentile.c. Compute the percentile rank of 71.
The following data give the numbers of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days.a. Calculate the values of the three quartiles and the interquartile range.b. Determine the (approximate) value of the 53rd percentile.c. Find the percentile rank
The following data give the numbers of minor penalties accrued by each of the 30 National Hockey League franchises during the 2010€“11 regular season.a. Calculate the values of the three quartiles and the interquartile range.b. Find the approximate value of the 57th percentile.c. Calculate the
The following data give the numbers of text messages sent by a high school student on 40 randomly selected days during 2012:a. Calculate the values of the three quartiles and the interquartile range. Where does the value 49 fall in relation to these quartiles? b. Determine the approximate value of
Nixon Corporation manufactures computer monitors. The following data give the numbers of computer monitors produced at the company for a sample of 30 days.a. Calculate the values of the three quartiles and the interquartile range. Where does the value of 31 lie in relation to these quartiles?b.
The following data give the numbers of new cars sold at a dealership during a 20-day period.a. Calculate the values of the three quartiles and the interquartile range. Where does the value of 4 lie in relation to these quartiles?b. Find the (approximate) value of the 25th percentile. Give a brief
According to www.money-zine.com, the average FICO score in the United States was around 692 in December 2011. Suppose the following data represent the credit scores of 22 randomly selected loan applicants.a. Calculate the values of the three quartiles and the interquartile range. Where does the

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