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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions
A discrete variable can take on only the values 0, 1, or 2. A set of 20 measurements on this variable is shown here:a. Construct a relative frequency histogram for the data.b. What proportion of the measurements are greater than 1?c. What proportion of the measurements are less than 2?d. If a
Identify each variable as quantitative or qualitative: a. Amount of time it takes to assemble a simple puzzle b. Number of students in a first-grade classroom c. Rating of a newly elected politician (excellent, good, fair, poor) d. State in which a person lives
Refer to Exercise 1.19.Exercise 1.19A discrete variable can take on only the values 0, 1, or 2. A set of 20 measurements on this variable is shown here:a. Draw a dotplot to describe the data. b. How could you define the stem and the leaf for this 4data set? c. Draw the stem and leaf plot using your
An experimental psychologist measured the length of time it took for a rat to successfully navigate a maze on each of 5 days. The results are shown in the table. Create a line chart to describe the data. Do you think that any learning is taking place?
The value of a quantitative variable is measured once a year for a 10-year period. Here are the data:a. Create a line chart to describe the variable as it changes over time. b. Describe the measurements using the chart constructed in part a.
Create a dotplot for the number of cheeseburgers consumed in a given week by 10 college students.a. How would you describe the shape of the distribution? b. What proportion of the students ate more than 4 cheese burgers that week?
The test scores on a 100-point test were recorded for 20 students:a. Use an appropriate graph to describe the data.b. Describe the shape and location of the scores.c. Is the shape of the distribution unusual? Can you think of any reason the distribution of the scores would have such a shape?
Altman and Bland report the survival times for patients with active hepatitis, half treated with prednisone and half receiving no treatment.7 The data that follow are adapted from their data for those treated with prednisone. The survival times are recorded to the nearest month:a. Look at the data.
The length of time (in months) between the onset of a particular illness and its recurrence was recorded for n = 50 patients:a. Construct a relative frequency histogram for the data.b. Would you describe the shape as roughly symmetric, skewed right, or skewed left?c. Give the fraction of recurrence
Education pays off, according to a snapshot provided by the Bureau of Labor Statistics. The median weekly earnings for six different levels of education are shown in the table:a. What graphical methods could you use to describe the data?b. Select the method from part a that you think best describes
The ages (in months) at which 50 children were first enrolled in a preschool are listed below.a. Construct a stem and leaf display for the data.b. Construct a relative frequency histogram for these data. Start the lower boundary of the first class at 30 and use a class width of 5 months.c. Compare
Statistics of the world's religions are only very rough approximations, since many religions do not keep track of their membership numbers. An estimate of these numbers (in millions) is shown in the table.a. Construct a pie chart to describe the total membership in the world's organized
Identify the following quantitative variables as discrete or continuous: a. Population in a particular area of the United States b. Weight of newspapers recovered for recycling on a single day c. Time to complete a sociology exam d. Number of consumers in a poll of 1000 who consider nutritional
To decide on the number of service counters needed for stores to be built in the future, a supermarket chain wanted to obtain information on the length of time (in minutes) required to service customers. To find the distribution of customer service times, a sample of 60 customers' service times was
Refer to Exercise 1.30. Construct a relative frequency histogram for the supermarket service times.Exercise 1.30To decide on the number of service counters needed for stores to be built in the future, a supermarket chain wanted to obtain information on the length of time (in minutes) required to
The calcium (Ca) content of a powdered mineral substance was analyzed 10 times with the following percent compositions recorded:a. Draw a dotplot to describe the data.b. Draw a stem and leaf plot for the data. Use the numbers in the hundredths and thousandths places as the stem.c. Are any of the
The following table lists the ages at the time of death for the 38 deceased American presidents from George Washington to Ronald Reagan:a. Construct a stem and leaf plot for the data. Describe the shape. Does it surprise you?b. The five youngest presidents at the time of death appear in the lower
The red blood cell count of a healthy person was measured on each of 15 days. The number recorded is measured in 106 cells per micro liter (µL).a. Use an appropriate graph to describe the data.b. Describe the shape and location of the red blood cell counts.c. If the person's red blood cell count
The officials of major league baseball have crowned a batting champion in the National League each year since 1876. A sample of winning batting averages is listed in the table:a. Construct a relative frequency histogram to describe the batting averages for these 20 champions. b. If you were to
The table that follows shows the weekend gross ticket sales for the top 20 movies for the weekend of June 25, 2010:a. Draw a stem and leaf plot for the data. Describe the shape of the distribution. Are there any outliers?b. Construct a dotplot for the data. Which of the two graphs is more
How safe is your neighborhood? Are there any hazardous waste sites nearby? The table shows the number of hazardous waste sites in each of the 50 states and the District of Columbia in the year 2009:a. What variable is being measured? Is the variable discrete or continuous? b. Describe the shape of
Identify each variable as quantitative or qualitative: a. Ethnic origin of a candidate for public office b. Score (0-100) on a placement examination c. Fast-food establishment preferred by a student (McDonald's, Burger King, or Carl's Jr.) d. Mercury concentration in a sample of tuna
Do you expect the distributions of the following variables to be symmetric or skewed? Explain. a. Size in dollars of non secured loans b. Size in dollars of secured loans c. Price of an 8-ounce can of peas d. Height in inches of freshman women at your university e. Number of broken taco shells in a
Identify each quantitative variable as discrete or continuous. a. Number of boating accidents along a 50-mile stretch of the Colorado River b. Time required to complete a questionnaire c. Cost of a head of lettuce d. Yield in kilograms of wheat from a 1-hectare plot in a wheat field.
Identify each variable as continuous or discrete: a. Number of homicides in Detroit during a 1-month period b. Length of time between arrivals at an outpatient clinic c. Number of typing errors on a page of manuscript d. Number of defective light-bulbs in a package containing four bulbs e. Time
Identify each variable as continuous or discrete: a. Weight of two dozen shrimp b. A person's body temperature c. Number of people waiting for treatment at a hospital emergency room d. Number of properties for sale by a real estate agency e. Number of claims received by an insurance company during
Identify each variable as continuous or discrete: a. Number of people in line at a supermarket checkout counter b. Depth of a snowfall c. Length of time for a driver to respond when faced with an impending collision d. Number of aircraft arriving at the Atlanta airport in a given hour
Aqua running has been suggested as a method of cardiovascular conditioning for injured athletes and others who want a low-impact aerobics program. A study reported in the Journal of Sports Medicine investigated the relationship between exercise cadence and heart rate by measuring the heart rates of
A lake is a body of water surrounded by land. Hence, some bodies of water named "seas," like the Caspian Sea, are actual salt lakes. In the table that follows, the length in miles is listed for the major natural lakes of the world, excluding the Caspian Sea, which has a length of 760 miles.a. Use a
We collected 50 pennies and recorded their ages, by calculatingAGE = CURRENT YEAR - YEAR ON PENNY.a. Before drawing any graphs, try to visualize what the distribution of penny ages will look like. Will it be mound-shaped, symmetric, skewed right, or skewed left? b. Draw a relative frequency
The data below represent the ages of a different set of 50 pennies, again calculated using AGE = CURRENT YEAR - YEAR ON PENNY.a. Draw a relative frequency histogram to describe the distribution of penny ages. Is the shape similar to the shape of the relative frequency histogram in Exercise 1.45?b.
Here is a list of the 44 presidents of the United States along with the number of regular vetoes used by each:Use an appropriate graph to describe the number of vetoes cast by the 44 presidents. Write a summary paragraph describing this set of data.
Are some cities more windy than others? Does Chicago deserve to be nicknamed "The Windy City"? These data are the average wind speeds (in miles per hour) for 54 selected cities in the United States:a. Construct a relative frequency histogram for the data.b. The value x = 35.1 was recorded at Mt.
The following data set shows the winning times (in seconds) for the Kentucky Derby races from 1950 to 2010.a. Do you think there will be a trend in the winning times over the years? Draw a line chart to verify your answer. b. Describe the distribution of winning times using an appropriate graph.
Six vehicles are selected from the vehicles that are issued campus parking permits, and the following data are recorded:a. What are the experimental units? b. What are the variables being measured? What types of variables are they? c. Is this univariate, bivariate, or multivariate data?
On April 20, 2010, the United States experienced a major environmental disaster when a Deepwater Horizon drilling rig exploded in the Gulf of Mexico. The number of personnel and equipment used in the Gulf oil spill cleanup, beginning May 2, 2010 (Day 13) through June 9, 2010 (Day 51) is given in
The 2008 election was a race in which Barack Obama defeated John McCain and other candidates, receiving 53% of the popular vote. The popular vote (in thousands) for Barack Obama in each of the 50 states is listed below:a. By just looking at the table, what shape do you think the data distribution
Refer to Exercise 1.51. Listed here is the percentage of the popular vote received by President Obama in each of the 50 states:Exercise 1.51 The 2008 election was a race in which Barack Obama defeated John McCain and other candidates, receiving 53% of the popular vote. The popular vote (in
The accompanying stem and leaf plots were generated using MINITAB for the variables named "Popular Vote" and "Percent Vote."For Information: Refer to Exercises 1.51 and 1.52.Exercises 1.51 and 1.52 Refer to Exercise 1.51. Listed here is the percentage of the popular vote received by President Obama
The self-reported heights of 105 students in a biostatistics class are described in the relative frequency histogram below.a. Describe the shape of the distribution. b. Do you see any unusual feature in this histogram? c. Can you think of an explanation for the two peaks in the histogram? Is there
Much of the world's diamond industry is located in Africa, with Russia and Canada also showing large revenues from their diamond mining industry. A visual representation of the various shares of the world's diamond revenues, adapted from Time Magazine, 15 is shown below:a. Draw a pie chart to
A group of 50 biomedical students recorded their pulse rates by counting the number of beats for 30 seconds and multiplying by 2.a. Why are all of the measurements even numbers?b. Draw a stem and leaf plot to describe the data, splitting each stem into two lines.c. Construct a relative frequency
Students at the University of California, Riverside (UCR), along with many other Californians love their Starbucks! The distances in miles from campus for the 41 Starbucks stores within 10 miles of UCR are shown below:Construct a relative frequency to describe the distances from the UCR campus,
In the spring of 2010, almost all of the 50 U.S. states plus the District of Columbia were facing drastic financial crises, with many planning across-the-board budget cuts, layoffs, higher education fees, and other strategies to cut next year's expected budget gap. The image that follows shows the
An article in Archaeometry involved an analysis of 26 samples of Romano-British pottery, found at four different kiln sites in the United Kingdom.18 The samples were analyzed to determine their chemical composition, and the percentage of aluminum oxide in each of the 26 samples is shown in the
A data set consists of the ages at death for each of the 38 past presidents of the United States now deceased. a. Is this set of measurements a population or a sample? b. What is the variable being measured? c. Is the variable in part b quantitative or qualitative?
Want to lose weight? You can do it by cutting calories, as long as you get enough nutritional value from the foods that you do eat! Below you will see a visual representation of the number of calories in some of America's favorite foods adapted from an article in The Press-Enterprise.a. Comment on
An informal experiment was conducted at McNair Academic High School in Jersey City, New Jersey, to investigate the use of laptop computers as a learning tool in the study of algebra.20 A freshman class of 20 students was given laptops to use at school and at home, while another freshman class of 27
The data below are the waiting times between eruptions of the Old Faithful geyser in Yellowstone National Park. Use one of the graphical methods from this chapter to describe the distribution of waiting times. If there are any unusual features in your graph, see if you can think of any practical
The following are the 2010 state gasoline tax in cents per gallon for the 50 U.S. states and the District of Columbia.a. Construct a stem and leaf display for the data.b. How would you describe the shape of this distribution?c. Are there states with unusually high or low gasoline taxes? If so,
The following data represent the planned rated capacities in megawatts (millions of watts) for the world's 20 largest hydroelectric plants.a. Construct a stem and leaf display for the data.b. How would you describe the shape of this distribution?
The most popular colors for compact and sports cars in a recent year are given in the table.Use an appropriate graphical display to describe these data.
The number of Starbucks coffee shops in cities within 20 miles of the University of California, Riverside is shown in the following table.a. Draw a dotplot to describe the data. b. Describe the shape of the distribution. c. Is there another variable that you could measure that might help to explain
The 98.6 degree standard for human body temperature was derived by a German doctor in 1868. In an attempt to verify his claim, Mackowiak, Wasserman, and Levine took temperatures from 148 healthy people over a 3-day period. A data set closely matching the one in Mackowiak's article was derived by
You are a candidate for your state legislature, and you want to survey voter attitudes regarding your chances of winning. Identify the population that is of interest to you and from which you would like to select your sample. How is this population dependent on time?
A medical researcher wants to estimate the survival time of a patient after the onset of a particular type of cancer and after a particular regimen of radiotherapy.a. What is the variable of interest to the medical researcher?b. Is the variable in part a qualitative, quantitative discrete, or
An educational researcher wants to evaluate the effectiveness of a new method for teaching reading to deaf students. Achievement at the end of a period of teaching is measured by a student's score on a reading test. a. What is the variable to be measured? What type of variable is it? b. What is the
Blood pressure is the pressure that the blood exerts against the walls of the arteries. When physicians or nurses measure your blood pressure, they take two readings. The systolic blood pressure is the pressure when the heart is contracting and therefore pumping. The diastolic blood pressure is the
You are given n = 5 measurements: 0, 5, 1, 1, 3. a. Draw a dotplot for the data. Guess the approximate "center." b. Find the mean, median, and mode. c. Locate the three measures of center on the dotplot in part a. Based on the relative positions of the mean and median, are the measurements
In a psychological experiment, the time on task was recorded for 10 subjects under a 5-minute time constraint. These measurements are in seconds:a. Find the average time on task.b. Find the median time on task.c. If you were writing a report to describe these data, which measure of central tendency
The number of Starbucks coffee shops in 21 cities within 20 miles of the University of California, Riverside is shown in the following table.a. Find the mean, the median, and the mode.b. Compare the median and the mean. What can you say about the shape of this distribution?c. Draw a dotplot for the
The "Wii" is an interactive gaming console popular among many gamers. Its cost can vary dramatically, depending on where it is purchased. The website www.pricegrabber .com lists l4 online sellers with various prices, including shipping and taxes:a. What is the average price of the Wii for these 14
You are given n = 5 measurements: 2, 1, 1, 3, 5.a. Calculate the sample mean, .b. Calculate the sample variance, s2, using the formula given by the definition.c. Find the sample standard deviation, s.d. Find s2 and s using the computing formula. Compare the results with those found in parts b and
You are given n = 8 measurements: 4, 1, 3, 1, 3, 1, 2, 2.a. Find the range.b. Calculate .c. Calculate s2 and s using the computing formula.
You are given n = 8 measurements: 3, 1, 5, 6, 4, 4, 3, 5. a. Calculate the range. b. Calculate the sample mean. c. Calculate the sample variance and standard deviation. d. Compare the range and the standard deviation. The range is approximately how many standard deviations?
An article in Archaeometry involved an analysis of 26 samples of Romano-British pottery found at four different kiln sites in the United Kingdom. The samples were analyzed to determine their chemical composition. The percentage of iron oxide in each of five samples collected at the Island Thorns
The monthly utility bills for a household in Riverside, California, were recorded for 12 consecutive months starting in January 2010:a. Calculate the range of the utility bills for the year 2010.b. Calculate the average monthly utility bill for the year 2010.c. Calculate the standard deviation for
A set of n = 10 measurements consists of the values 5, 2, 3, 6, 1, 2, 4, 5, 1, 3. a. Use the range approximation to estimate the value of s for this set. b. Use your calculator to find the actual value of s. Is the actual value close to your estimate in part a? c. Draw a dotplot of this data set.
You are given n 8 measurements: 3, 2, 5, 6, 4, 4, 3, 5.a. Find .b. Find m.c. Based on the results of parts a and b, are the measurements symmetric or skewed? Draw a dotplot to confirm your answer.
Suppose you want to create a mental picture of the relative frequency histogram for a large data set consisting of 1000 observations, and you know that the mean and standard deviation of the data set are 36 and 3, respectively.a. If you are fairly certain that the relative frequency distribution of
A distribution of measurements is relatively mound-shaped with mean 50 and standard deviation 10.a. What proportion of the measurements will fall between 40 and 60?b. What proportion of the measurements will fall between 30 and 70?c. What proportion of the measurements will fall between 30 and
A set of data has a mean of 75 and a standard deviation of 5. You know nothing else about the size of the data set or the shape of the data distribution.a. What can you say about the proportion of measurements that fall between 60 and 90?b. What can you say about the proportion of measurements that
The length of time required for an automobile driver to respond to a particular emergency situation was recorded for n = 10 drivers. The times (in seconds) were .5, .8, 1.1, .7, .6, .9, .7, .8, .7, .8.a. Scan the data and use the procedure in Section 2.5 to find an approximate value for s. Use this
The data listed here are the weights (in pounds) of 27 packages of ground beef in a supermarket meat display:a. Construct a stem and leaf plot or a relative frequency histogram to display the distribution of weights. Is the distribution relatively mound-shaped?b. Find the mean and standard
Is your breathing rate normal? Actually, there is no standard breathing rate for humans. It can vary from as low as 4 breaths per minute to as high as 70 or 75 for a person engaged in strenuous exercise. Suppose that the resting breathing rates for college-age students have a relative frequency
A geologist collected 20 different ore samples, all the same weight, and randomly divided them into two groups. She measured the titanium (Ti) content of the samples using two different methods.a. Construct stem and leaf plots for the two data sets. Visually compare their centers and their
A group of 70 students were asked to record the last digit of their social security number.a. Draw a relative frequency histogram using the values 0 through 9 as the class midpoints. What is the shape of the distribution? Based on the shape, what would be your best estimate for the mean of the data
Refer to the data set in Exercise 2.27.Exercise 2.27A group of 70 students were asked to record the last digit of their social security number.a. Find the percentage of measurements in the intervals ± s, ± 2s, and ± 3s.b. How do the percentages obtained in part a compare with those given by
A group of laboratory animals is infected with a particular form of bacteria, and their survival time is found to average 32 days, with a standard deviation of 36 days. a. Visualize the distribution of survival times. Do you think that the distribution is relatively mound-shaped, skewed right, or
You are given n = 10 measurements: 3, 5, 4, 6, 10, 5, 6, 9, 2, 8. a. Calculate . b. Find m. c. Find the mode.
Refer to Exercise 2.29. You can use the Empirical Rule to see why the distribution of survival times could not be mound-shaped. Exercise 2.29 A group of laboratory animals is infected with a particular form of bacteria, and their survival time is found to average 32 days, with a standard deviation
To estimate the amount of lumber in a tract of timber, an owner decided to count the number of trees with diameters exceeding 12 inches in randomly selected 50-by-50-foot squares. Seventy 50-by-50-foot squares were chosen, and the selected trees were counted in each tract. The data are listed
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.For Information: Refer to Exercise 2.8 and data set EX0208.a. Use the range approximation to find an estimate of s. b. How does
The data below are 30 waiting times between eruptions of the Old Faithful geyser in Yellowstone National Park.a. Calculate the range.b. Use the range approximation to approximate the standard deviation of these 30 measurements.c. Calculate the sample standard deviation s.d. What proportion of the
The table below shows the names of the 43 presidents of the United States along with the number of their children.a. Construct a relative frequency histogram to describe the data. How would you describe the shape of this distribution?b. Calculate the mean and the standard deviation for the data
The percentage of iron oxide in each of five pottery samples collected at the Island Thorns site was:a. Use the range approximation to find an estimate of s, using an appropriate divisor from Table 2.7. b. Calculate the standard deviation s. How close did your estimate come to the actual value of
The number of passes completed by Aaron Rodgers, quarterback for the Minnesota Vikings, was recorded for each of the 15 regular season games that he played in the fall of 2010 (www.ESPN.com):a. Draw a stem and leaf plot to describe the data.b. Calculate the mean and standard deviation for Aaron
Suppose that some measurements occur more than once and that the data x1, x2,..., xk are arranged in a frequency table as shown here:The formulas for the mean and variance for grouped data are Notice that if each value occurs once, these formulas reduce to those given in the text. Although these
High school students in an International Baccalaureate (IB) program are placed in accelerated or advanced courses and must take IB examinations in each of six subject areas at the end of their junior or senior year. Students are scored on a scale of 1-7, with 1-2 being poor, 3 mediocre, 4 average,
To illustrate the utility of the Empirical Rule, consider a distribution that is heavily skewed to the right, as shown in the accompanying figure.a. Calculate and s for the data shown.b. Construct the intervals ± s, ± 2s, and ± 3s and locate them on the frequency distribution.c. Calculate the
The cost of automobile insurance has become a sore subject in California because insurance rates are dependent on so many different variables, such as the city in which you live, the number of cars you insure, and the company with which you are insured. The website www.insurance.ca.gov reports the
Given the following data set: 8, 7, 1, 4, 6, 6, 4, 5, 7, 6, 3, 0a. Find the five-number summary and the IQR.b. Calculate and s.c. Calculate the z-score for the smallest and largest observations. Is either of these observations unusually large or unusually small?
Find the five-number summary and the IQR for these data:
Given the following data set: 2.3, 1.0, 2.1, 6.5, 2.8, 8.8, 1.7, 2.9, 4.4, 5.1, 2.0 a. Find the positions of the lower and upper quartiles. b. Sort the data from smallest to largest and find the lower and upper quartiles. c. Calculate the IQR.
Given the following data set: .23, .30, .35, .41, .56, .58, .76, .80 a. Find the lower and upper quartiles. b. Calculate the IQR. c. Calculate the lower and upper fences. Are there any outliers?
Construct a box plot for these data and identify any outliers:
Construct a box plot for these data and identify any outliers:
Environmental scientists are increasingly concerned with the accumulation of toxic elements in marine mammals and the transfer of such elements to the animals' offspring. The striped dolphin (Stenella coeruleoalba), considered to be a top predator in the marine food chain, was the subject of one
The weights (in pounds) of the 27 packages of ground beef from Exercise 2.24 (see data set EX0224) are listed here in order from smallest to largest:a. Confirm the values of the mean and standard deviation, calculated in Exercise 2.24 as = 1.05 and s = .17. b. The two largest packages of meat
How does Aaron Rodgers, quarterback for the 2011 Super Bowl winners, the Green Bay Packers, compare to Drew Brees, quarterback for the 2010 Super Bowl winners, the New Orleans Saints? The table below shows the number of completed passes for each athlete during the 2010 NFL football season:a.
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