Muzzle Velocity The following data represent the muzzle

Problem 1CT The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab (a) Determine the mean amount of time spent doing Section homework. ________________ (b) Determine the median amount of time spent doing Section homework. ________________ (c) Suppose the observation 109 minutes is incorrectly recorded as 1009 minutes. Recompute the mean and the median. What do you notice? What property of the median does this illustrate?

Problem 1RE Muzzle Velocity The following data represent the muzzle velocity (in meters per second) of rounds fired from a 155-mm gun. 793.8 793.1 792.4 794.0 791.4 792.4 791.7 792.3 789.6 794.4 Source: Christenson. Ronald, and Blackwood. Larry. “Tests for Precision and Accuracy of Multiple Measuring Devices,” Technometrics. 35(4): 411-421,1993. (a) Compute the sample mean and median muzzle velocity. ________________ (b) Compute the range, sample variance, and sample standard deviation.

Problem 2CT The Federal Bureau of Investigation classifies various larcenies. The following data represent the type of larcenies based on a random sample of 15 larcenies. What is the mode type of larceny? Pocket picking and purse snatching Bicycles From motor vehicles From motor vehicles From motor vehicles From buildings From buildings Shoplifting Motor vehicle accessories From motor vehicles Shoplifting From motor vehicles From motor vehicles Pocket picking and purse snatching From motor vehicles

Problem 3CT Determine the range of the homework data from. The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab

Problem 3RE Chief Justices The following data represent the ages of chief justices of the U.S. Supreme Court when they were appointed. Justice Age John Jay 44 John Rutledge 56 Oliver Ellsworth 51 John Marshall 46 Roger B. Taney 59 Salmon P. Chase 56 Morrison R. Waite 58 Melville W. Fuller 55 Edward D. White 65 William H. Taft 64 Charles E. Hughes 68 Harlan F. Stone 69 Frederick M. Vinson 56 Earl Warren 62 Warren E. Burger 62 William H. Rehnquist 62 John G. Roberts 50 Source. Information Please Almanac (a) Determine the population mean, median, and mode ages. ________________ (b) Determine the range and population standard deviation ages. ________________ (c) Obtain two simple random samples of size 4, and determine the sample mean and sample standard deviation ages.

Problem 5CT In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340. (a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to the Empirical_Rule, 99.7% of toner cartridges will print between and pages. ________________ (b) Assuming that the distribution of the data are bell shaped, determine the percentage of toner cartridges whose print total is between 3622 and 4982 pages. ________________ (c) If the company that manufactures the toner cartridges guarantees to replace any cartridge that does not print at least 3622 pages, what percent of cartridges can the firm expect to be responsible for replacing, according to the Empirical Rule? ________________ (d) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean. ________________ (e) Use Chebyshev’s inequality to determine the minimum percentage of toner cartridges that print between 3282 and 5322 pages.

Problem 4RE Number of Tickets Issued As part of a statistics project, a student surveys 30 randomly selected students and asks them how many speeding tickets they have been issued in the past month. The results of the survey are as follows: 1 1 0 1 0 0 0 0 0 1 0 1 0 1 2 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 (a) Draw a frequency histogram of the data and describe its shape. ________________ (b) Based on the shape of the histogram, do you expect the mean to be more than, equal to, or less than the median? ________________ (c) Determine the mean and the median of the number of tickets issued. ________________ (d) Determine the mode of the number of tickets issued.

Problem 2RE Price of Chevy Cobalts The following data represent the sales price in dollars for nine 2-year-old Chevrolet Cobalts in the Los Angeles area. 14050 13999 12999 10995 9980 8998 7889 7200 5500 Source: cars.com (a) Determine the sample mean and median price. ________________ (b) Determine the range, sample standard deviation, and interquartile range. ________________ (c) Redo (a) and (b) if the data value 14,050 was incorrectly entered as 41,050. How does this change affect the mean? The median? the range? the standard deviation? the interquartile range? Which of these values is resistant?

Problem 4CT (a) Determine the standard deviation of the homework data from ________________ The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab (b) By hand, determine and interpret the interquartile range of the homework data from Problem. ________________ The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab (c) Which of these two measures of dispersion is resistant? Why? Problem The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Section, Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab (a) Determine the mean amount of time spent doing Section homework. ________________ (b) Determine the median amount of time spent doing Section homework. ________________ (c) Suppose the observation 109 minutes is incorrectly recorded as 1009 minutes. Recompute the mean and the median. What do you notice? What property of the median does this illustrate?

Problem 5RE Chebyshev’s Inequality and the Empirical Rule Suppose that a certain brand of light bulb has a mean life of 600 hours and a standard deviation of 53 hours. (a) A histogram of the data indicates the sample data follow a bell-shaped distribution. According to the Empirical Rule, 99.7% of light bulbs have lifetimes between ______ and ______ hours. ________________ (b) Assuming the data are bell shaped, determine the percentage of light bulbs that will have a life between 494 and 706 hours. ________________ (c) Assuming the data are bell shaped, what percentage of light bulbs will last between 547 and 706 hours. ________________ (d) If the company that manufactures the light bulb guarantees to replace any bulb that does not last at least 441 hours, what percentage of light bulbs can the firm expect to have to replace, according to the Empirical Rule? ________________ (e) Use Chebyshev’s Inequality to determine the minimum percentage of light bulbs with a life within 2.5 standard deviations of the mean. ________________ (f ) Use Chebyshev’s Inequality to determine the minimum percentage of light bulbs with a life between 494 and 706 hours.

Problem 6CT The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park. Time (minutes) Frequency 40–49 8 50–59 44 60–69 23 70–79 6 80–89 107 90–99 11 100–109 1 (a) Approximate the mean length of time between eruptions. ________________ (b) Approximate the standard deviation length of time between eruptions.

Problem 6RE Travel Time to Work The frequency distribution listed in the table represents the travel time to work (in minutes) for a random sample of 895 U.S. adults. Travel Time (minutes) Frequency 0-9 125 10-19 271 20-29 186 30-39 121 40-49 54 50-59 62 60-69 43 70-79 20 80-89 13 Source: Based on data from the 2009 American Community Survey (a) Approximate the mean travel time to work for U.S. adults. ________________ (b) Approximate the standard deviation travel time to work for U.S. adults.

Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost $2.70 per pound), 1 pound of ground turkey (cost $1.30 per pound), and \(\frac{1}{2}\) pound of ground pork (cost $1.80 per pound). What is the cost per pound of the meatloaf? Equation Transcription: Text Transcription: \frac{1}{2}

Problem 7RE Weighted Mean Michael has just completed his first semester in college. He earned an A in his 5-hour calculus course, a B in his 4-hour chemistry course, an A in his 3-hour speech course, and a C in his 3-hour psychology course. Assuming an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Michael’s grade-point average if grades are weighted by class hours.

Problem 8RE Weights of Males versus Females According to the National Center for Health Statistics, the mean weight of a 20- to 29-year-old female is 156.5 pounds, with a standard deviation of 51.2 pounds. The mean weight of a 20- to 29-year-old male is 183.4 pounds, with a standard deviation of 40.0 pounds. Who is relatively heavier: a 20- to 29-year-old female who weighs 160 pounds or a 20- to 29-year-old male who weighs 185 pounds?

Problem 9CT The following data represent the weights (in grams) of 50 randomly selected quarters. Determine and interpret the quartiles. Does the data set contain any outliers? 5.49 5.58 5.60 5.62 5.68 5.52 5.58 5.60 5.63 5.70 5.53 5.58 5.60 5.63 5.71 5.53 5.58 5.60 5.63 5.71 5.53 5.58 5.60 5.65 5.72 5.56 5.58 5.60 5.66 5.73 5.57 5.59 5.60 5.66 5.73 5.57 5.59 5.61 5.66 5.73 5.57 5.59 5.62 5.67 5.74 5.57 5.59 5.62 5.67 5.84

Problem 8CT An engineer is studying bearing failures for two different materials in aircraft gas turbine engines. The following data are failure times (in millions of cycles) for samples of the two material types. Material A Material B 3.17 5.88 5.78 9.65 4.31 6.91 6.71 13.44 4.52 8.01 6.84 14.71 4.66 8.97 7.23 16.39 5.69 11.92 8.20 24.37 (a) Determine the sample mean failure time for each material. ________________ (b) By hand, compute the median failure time for each material. ________________ (c) Determine the sample standard deviation of the failure times for each material. Which material has its failure times more dispersed? ________________ (d) By hand, compute the five-number summary for each material. ________________ (e) On the same graph, draw boxplots for the two materials. Annotate the graph with some general remarks comparing the failure times. ________________ (f ) Describe the shape of the distribution of each material using the boxplot and quartiles.

Halladay No-No On October 6, 2010, Roy Halladay of the Philadelphia Phillies threw the second post-season no-hitter in major league history. The side-by-side boxplot shows the pitch speed (in miles per hour) for all of Halladay’s pitches during the game. (a) Which pitch is typically thrown the fastest? (b) Which pitch is most erratic as far as pitch speed goes? (c) Which pitch is most consistent as far as pitch speed goes, the cut fastball or the four-seam fastball? (d) Are there any outliers for Halladay’s cut fastball? If so, approximate the pitch speed of the outlier. (e) Describe the shape of the distribution of Halladay’s curveball. (f ) Describe the shape of the distribution of Halladay’s four-seam fastball.

Problem 10CT Armando is filling out a college application. The application requires that Armando supply either his SAT math score or his ACT math score. Armando scored 610 on the SAT math and 27 on the ACT math. Which score should Armando report, given that the mean SAT math score is 515 with a standard deviation of 114, and the mean ACT math score is 21.0 with a standard deviation of 5.1? Why?

Problem 11CT According to the National Center for Health Statistics, a 10-year-old male whose height is 53.5 inches has a height that is at the 15th percentile. Explain what this means.

Problem 10RE Presidential Inaugural Addresses Ever wonder how many words are in a typical inaugural address? The following data represent the lengths of all the inaugural addresses (measured in word count) for all presidents up to Barack Obama. 1425 1125 1128 5433 2242 2283 135 1172 1337 1802 2446 1507 2308 3838 2480 1526 2449 2170 1729 8445 2978 3318 1355 1571 2158 4776 1681 4059 1437 2073 1175 996 4388 3801 2130 2406 1209 3319 2015 1883 1668 3217 2821 3967 1807 1087 4467 3634 2217 1340 2463 2906 698 985 559 2546 Source: infoplease.com (a) Determine the mean and median number of words in a presidential inaugural address. ________________ (b) Determine and interpret the quartiles for the number of words in a presidential inaugural address. ________________ (c) Determine the five-number summary for the number of words in a presidential inaugural address. ________________ (d) Determine the standard deviation and interquartile range for the number of words in a presidential inaugural address. ________________ (e) Are there any outliers in the data set? If so, what is (are) the value(s)? ________________ (f) Draw a boxplot of the data. ________________ (g) Describe the shape of the distribution. Support your position using the boxplot and quartiles. ________________ (h) Which measure of central tendency do you think better describes the typical number of words in an inaugural address? Why? ________________ (i) Which measure of dispersion do you think better describes the spread of the typical number of words in an inaugural address? Why?

Problem 11RE You Explain It! Percentiles According to the National Center for Health Statistics, a 19-year-old female whose height is 67.1 inches has a height that is at the 85th percentile. Explain what this means.

Problem 12CT The distribution of income tends to be skewed to the right. Suppose you are running for a congressional seat and wish to portray that the average income in your district is low. Which measure of central tendency, the mean or the median, would you report? Why?

Problem 12RE Skinfold Thickness Procedure One method of estimating body fat is through skinfold thickness measurement. The measurement can use from three to nine different standard anatomical sites around the body. The right side is usually only measured (for consistency). The tester pinches the skin at the appropriate site to raise a double layer of skin and the underlying adipose tissue, but not the muscle. Calipers are then applied 1 centimeter below and at right angles to the pinch and a reading is taken 2 seconds later. The mean of two measurements should be taken. If the two measurements differ greatly, a third should be done and then the median value taken. Explain why a median is used as the measure of central tendency when three measures are taken, rather than the mean.

Answer the following based on the histograms shown to the right. (a) Which measure of central tendency would you recommend reporting for the data whose histogram is shown in Figure I? Why? (b) Which one has more dispersion? Explain.

The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivans Intermediate Algebra course spent on the homework from Section 4.5, Factoring Polynomials. 48 88 57 109 111 93 71 63 Source: MyMathLab CHAPTER TEST (a) Determine the mean amount of time spent doing Section 4.5 homework. (b) Determine the median amount of time spent doing Section 4.5 homework. (c) Suppose the observation 109 minutes is incorrectly recorded as 1009 minutes. Recompute the mean and the median. What do you notice? What property of the median does this illustrate?

based on a random sample of 15 larcenies. What is the mode type of larceny? Pocket picking and purse snatching Bicycles From motor vehicles From motor vehicles From motor vehicles From buildings From buildings Shoplifting Motor vehicle accessories From motor vehicles Shoplifting From motor vehicles From motor vehicles Pocket picking and purse snatching From motor vehicles

Determine the range of the homework data from Problem 1

(a) Determine the standard deviation of the homework data from Problem 1. (b) By hand, determine and interpret the interquartile range of the homework data from Problem 1. (c) Which of these two measures of dispersion is resistant? Why?

In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340. (a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to the Empirical Rule, 99.7% of toner cartridges will print between and pages. (b) Assuming that the distribution of the data are bell shaped, determine the percentage of toner cartridges whose print total is between 3622 and 4982 pages. (c) If the company that manufactures the toner cartridges guarantees to replace any cartridge that does not print at least 3622 pages, what percent of cartridges can the firm expect to be responsible for replacing, according to the Empirical Rule? (d) Use Chebyshevs inequality to determine the minimum percentage of toner cartridges with a page count within 1.5 standard deviations of the mean. (e) Use Chebyshevs inequality to determine the minimum percentage of toner cartridges that print between 3282 and 5322 pages

The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park. Time (minutes) Frequency 4049 8 5059 44 6069 23 7079 6 8089 107 9099 11 100109 1 (a) Approximate the mean length of time between eruptions. (b) Approximate the standard deviation length of time between eruptions.

Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost $2.70 per pound), 1 pound of ground turkey (cost $1.30 per pound), and 1 2 pound of ground pork (cost $1.80 per pound). What is the cost per pound of the meatloaf?

An engineer is studying bearing failures for two different materials in aircraft gas turbine engines. The following data are failure times (in millions of cycles) for samples of the two material types. Material A Material B 3.17 5.88 5.78 9.65 4.31 6.91 6.71 13.44 4.52 8.01 6.84 14.71 4.66 8.97 7.23 16.39 5.69 11.92 8.20 24.37 (a) Determine the sample mean failure time for each material. (b) By hand, compute the median failure time for each material. (c) Determine the sample standard deviation of the failure times for each material. Which material has its failure times more dispersed? (d) By hand, compute the five-number summary for each material. (e) On the same graph, draw boxplots for the two materials. Annotate the graph with some general remarks comparing the failure times. (f ) Describe the shape of the distribution of each material using the boxplot and quartiles.

The following data represent the weights (in grams) of 50 randomly selected quarters. Determine and interpret the quartiles. Does the data set contain any outliers? 5.49 5.58 5.60 5.62 5.68 5.52 5.58 5.60 5.63 5.70 5.53 5.58 5.60 5.63 5.71 5.53 5.58 5.60 5.63 5.71 5.53 5.58 5.60 5.65 5.72 5.56 5.58 5.60 5.66 5.73 5.57 5.59 5.60 5.66 5.73 5.57 5.59 5.61 5.66 5.73 5.57 5.59 5.62 5.67 5.74 5.57 5.59 5.62 5.67 5.84

Armando is filling out a college application. The application requires that Armando supply either his SAT math score or his ACT math score. Armando scored 610 on the SAT math and 27 on the ACT math. Which score should Armando report, given that the mean SAT math score is 515 with a standard deviation of 114, and the mean ACT math score is 21.0 with a standard deviation of 5.1? Why?

According to the National Center for Health Statistics, a 10-year-old male whose height is 53.5 inches has a height that is at the 15th percentile. Explain what this means.

The distribution of income tends to be skewed to the right. Suppose you are running for a congressional seat and wish to portray that the average income in your district is low. Which measure of central tendency, the mean or the median, would you report? Why?

Answer the following based on the histograms shown to the right. (a) Which measure of central tendency would you recommend reporting for the data whose histogram is shown in Figure I? Why? (b) Which one has more dispersion? Explain.