Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 3.3, Problem 2E
Define percentile rank.
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17. Suppose that X1, X2,..., Xn are random variables, such that E|xk| < ∞ for
all k, and set Yn = max1
6. Show that, for any random variable, X, and a > 0,
L
P(x < X ≤ x+a) dx = a.
2015
15. This problem extends Problem 20.6. Let X, Y be random variables with finite
mean. Show that
(P(X ≤ x ≤ Y) - P(Y < x ≤ X))dx = E Y — E X.
Chapter 3 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 3.1 - Teacher Salaries The following data from several...Ch. 3.1 - Roller Coaster Speeds The data show the heights in...Ch. 3.1 - Airport Parking The number of short-term parking...Ch. 3.1 - Length of School Years The lengths of school years...Ch. 3.1 - Observers in the Frogwatch Program The number of...Ch. 3.1 - Top Video Games The following represent XBOX One...Ch. 3.1 - Earnings of Nonliving Celebrities Forbes magazine...Ch. 3.1 - Paid Days Off The data show the number of paid...Ch. 3.1 - Top-Paid CEOs The data shown are the total...Ch. 3.1 - Airline Passengers The data show a sample of the...
Ch. 3.1 - Foreign Workers The number of foreign workers...Ch. 3.1 - Distances of Stars Of the 25 brightest stars, the...Ch. 3.1 - Contest Spelling Words The last words given and...Ch. 3.1 - Wind Speeds The data show the maximum wind speeds...Ch. 3.1 - Hourly Compensation for Production Workers The...Ch. 3.1 - Points in Rose Bowl Games The data show the number...Ch. 3.1 - Percentage of Foreign-Born People The percentage...Ch. 3.1 - Percentage of College-Educated Population over 25...Ch. 3.1 - Net Worth of Corporations These data represent the...Ch. 3.1 - Specialty Coffee Shops A random sample of 30...Ch. 3.1 - Commissions Earned This frequency distribution...Ch. 3.1 - Children of U.S. Presidents The data show the...Ch. 3.1 - Enrollments for Selected Independent Religiously...Ch. 3.1 - Automobile Selling Prices Find the weighted mean...Ch. 3.1 - Fat Grams Using the weighted mean, find the...Ch. 3.1 - Diet Cola Preference A recent survey of a new diet...Ch. 3.1 - Costs of Helicopters The costs of three models of...Ch. 3.1 - Final Grade An instructor grades exams, 20%; term...Ch. 3.1 - Final Grade Another instructor gives four 1-hour...Ch. 3.1 - For these situations, state which measure of...Ch. 3.1 - Describe which measure of central tendencymean,...Ch. 3.1 - What types of symbols are used to represent sample...Ch. 3.1 - A local fast-food company claims that the average...Ch. 3.1 - If the mean of five values is 64, find the sum of...Ch. 3.1 - If the mean of five values is 8.2 and four of the...Ch. 3.1 - Find the mean of 10, 20, 30, 40, and 50. a. Add 10...Ch. 3.1 - Harmonic Mean The harmonic mean (HM) is defined as...Ch. 3.1 - Geometric Mean The geometric mean (GM) is defined...Ch. 3.1 - Quadratic Mean A useful mean in the physical...Ch. 3.1 - Median for Grouped Data An approximate median can...Ch. 3.2 - Blood Pressure The table lists means and standard...Ch. 3.2 - What is the relationship between the variance and...Ch. 3.2 - Why might the range not be the best estimate of...Ch. 3.2 - What are the symbols used to represent the...Ch. 3.2 - What are the symbols used to represent the sample...Ch. 3.2 - Why is the unbiased estimator of variance used?Ch. 3.2 - The three data sets have the same mean and range,...Ch. 3.2 - Traveler Spending The data show the traveler...Ch. 3.2 - Cigarette Taxes The increases (in cents) in...Ch. 3.2 - Prob. 9ECh. 3.2 - Size of U.S. States The total surface area (in...Ch. 3.2 - Multiple Births The numbers of various multiple...Ch. 3.2 - Starting Teachers Salaries Starting teachers...Ch. 3.2 - Ages of U.S. Astronaut Candidates The average age...Ch. 3.2 - Times Spent in Rush-Hour Traffic A sample of 12...Ch. 3.2 - Laws Passed The data show the number of public...Ch. 3.2 - Passenger Vehicle Deaths The number of people...Ch. 3.2 - Annual Precipitation Days The number of annual...Ch. 3.2 - Use the data from Exercises 7, 15, and 17...Ch. 3.2 - Pupils Per Teacher The following frequency...Ch. 3.2 - Automotive Fuel Efficiency Thirty automobiles were...Ch. 3.2 - Murders in Cities The data show the number of...Ch. 3.2 - Reaction Times In a study of reaction times to a...Ch. 3.2 - FM Radio Stations A random sample of 30 states...Ch. 3.2 - Murder Rates The data represent the murder rate...Ch. 3.2 - Waterfall Heights The frequency distribution shows...Ch. 3.2 - Baseball Team Batting Averages Team batting...Ch. 3.2 - Missing Work The average number of days that...Ch. 3.2 - Suspension Bridges The lengths (in feet) of the...Ch. 3.2 - Hospital Emergency Waiting Times The mean of the...Ch. 3.2 - Ages of Accountants The average age of the...Ch. 3.2 - Using Chebyshevs theorem, solve these problems for...Ch. 3.2 - The mean of a distribution is 20 and the standard...Ch. 3.2 - In a distribution of 160 values with a mean of 72,...Ch. 3.2 - Calories in Bagels The average number of calories...Ch. 3.2 - Time Spent Online Americans spend an average of 3...Ch. 3.2 - Solid Waste Production The average college student...Ch. 3.2 - Sale Price of Homes The average sale price of...Ch. 3.2 - Trials to Learn a Maze The average of the number...Ch. 3.2 - Farm Sizes The average farm in the United States...Ch. 3.2 - Citrus Fruit Consumption The average U.S. yearly...Ch. 3.2 - SAT Scores The national average for mathematics...Ch. 3.2 - Work Hours for College Faculty The average...Ch. 3.2 - Prices of Musical Instruments The average price of...Ch. 3.2 - Hours of Employment The mean and standard...Ch. 3.2 - Prob. 45ECh. 3.2 - Bonuses The mean and standard deviation of the...Ch. 3.2 - Serum Cholesterol Levels For this data set, find...Ch. 3.2 - Ages of Consumers For this data set, find the mean...Ch. 3.2 - Prob. 49ECCh. 3.2 - Use this data set: 10, 20, 30, 40, 50 a. Find the...Ch. 3.2 - Mean Deviation The mean deviation is found by...Ch. 3.2 - Pearson Coefficient of Skewness A measure to...Ch. 3.2 - All values of a data set must be within sn1 of the...Ch. 3.3 - Determining Dosages In an attempt to determine...Ch. 3.3 - What is a z score?Ch. 3.3 - Define percentile rank.Ch. 3.3 - What is the difference between a percentage and a...Ch. 3.3 - Define quartile.Ch. 3.3 - What is the relationship between quartiles and...Ch. 3.3 - What is a decile?Ch. 3.3 - How are deciles related to percentiles?Ch. 3.3 - To which percentile, quartile, and decile does the...Ch. 3.3 - Vacation Days If the average number of vacation...Ch. 3.3 - Age of Senators The average age of Senators in the...Ch. 3.3 - Marriage Age for Females The mean age at which...Ch. 3.3 - Teachers Salary The average teachers salary in a...Ch. 3.3 - Test Scores Which is a better relative position, a...Ch. 3.3 - College and University Debt A student graduated...Ch. 3.3 - Annual Miles Driven The average miles driven...Ch. 3.3 - Which score indicates the highest relative...Ch. 3.3 - The data show the population (in thousands) for a...Ch. 3.3 - College Room and Board Costs Room and board costs...Ch. 3.3 - Achievement Test Scores The data shown represent...Ch. 3.3 - Airplane Speeds The airborne speeds in miles per...Ch. 3.3 - Average Weekly Earnings The average weekly...Ch. 3.3 - Test Scores Find the percentile rank for each test...Ch. 3.3 - Hurricane Damage Find the percentile rank for each...Ch. 3.3 - Test Scores Find the percentile rank for each test...Ch. 3.3 - Taxes The data for a recent year show the taxes...Ch. 3.3 - Medical Marijuana 2015 Sales Tax: The data show...Ch. 3.3 - Gold Reserves The data show the gold reserves for...Ch. 3.3 - Police Calls in Schools The number of incidents in...Ch. 3.3 - Check each data set for outliers. a. 46, 28, 32,...Ch. 3.3 - Check each data set for outliers. a. 88, 72, 97,...Ch. 3.3 - Another measure of the average is called the...Ch. 3.3 - An employment evaluation exam has a variance of...Ch. 3.3 - A particular standardized test has scores that...Ch. 3.4 - Applying the Concepts 34 The Noisy Workplace...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 16, identify the five-number summary...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 710, use each boxplot to identify...Ch. 3.4 - For Exercises 7-10. use each boxplot to identify-...Ch. 3.4 - School Graduation Rates The data show a sample of...Ch. 3.4 - Innings Pitched Construct a boxplot for the...Ch. 3.4 - Population of Colonies The data show the...Ch. 3.4 - Visitors Who Travel to Foreign Countries Construct...Ch. 3.4 - Areas of Islands The data show the sizes in square...Ch. 3.4 - Size of Dams These data represent the volumes in...Ch. 3.4 - Largest Dams The data show the heights (in feet)...Ch. 3.4 - Number of Tornadoes A four-month record for the...Ch. 3.4 - Unhealthy Smog Days A modified boxplot can be...Ch. 3 - Bank Failures The data show the number of bank...Ch. 3 - Shark Attacks The number of shark attacks and...Ch. 3 - AID: 1825 | 29/05/2018 3. Systolic Blood Pressure...Ch. 3 - SAT Scores The mean SAT math scores for selected...Ch. 3 - Households of Four Television Networks A survey...Ch. 3 - Investment Earnings An investor calculated these...Ch. 3 - Confirmed Measles Cases The data show a sample of...Ch. 3 - Tallest Buildings The number of stories in the 13...Ch. 3 - Rise in Tides Shown here is a frequency...Ch. 3 - Fuel Capacity The fuel capacity in gallons for...Ch. 3 - If the range of a data set is 24, find the...Ch. 3 - If the range of a data set is 56, find the...Ch. 3 - Textbooks in Professors Offices If the average...Ch. 3 - Magazines in Bookstores A survey of bookstores...Ch. 3 - Cost of Car Rentals A survey of car rental...Ch. 3 - AID: 1825 | 28/05/2018 16. Average Earnings of...Ch. 3 - Labor Charges The average labor charge for...Ch. 3 - Costs to Train Employees For a certain type of...Ch. 3 - Cost of a Mans Haircut The average cost of a mans...Ch. 3 - Exam Completion Time The mean time it takes a...Ch. 3 - Cases of Meningitis The data show the number of...Ch. 3 - Exam Grades Which of these exam grades has a...Ch. 3 - The number of police calls a small police...Ch. 3 - Printer Repairs The frequency distribution shows...Ch. 3 - Check each data set for outliers. a. 506, 511,...Ch. 3 - Check each data set for outliers. a. 14, 18, 27,...Ch. 3 - Named Storms The data show the number of named...Ch. 3 - Hours Worked The data shown here represent the...Ch. 3 - From the Data Bank, choose one of the following...Ch. 3 - Prob. 2DACh. 3 - Prob. 3DACh. 3 - Randomly select 10 values from the number of...Ch. 3 - Prob. 5DACh. 3 - AID: 1825 | 28/05/2018 Determine whether each...Ch. 3 - Prob. 2CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 4CQCh. 3 - In a data set, the mode will always be unique.Ch. 3 - Prob. 6CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 8CQCh. 3 - Determine whether each statement is true or false....Ch. 3 - Prob. 10CQCh. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Which is not part of the five-number summary? a....Ch. 3 - A statistic that tells the number of standard...Ch. 3 - When a distribution is bell-shaped, approximately...Ch. 3 - Prob. 16CQCh. 3 - Generally, Greek letters are used to represent...Ch. 3 - Prob. 18CQCh. 3 - The symbol for the population standard deviation...Ch. 3 - When the sum of the lowest data value and the...Ch. 3 - If the mode is to the left of the median and the...Ch. 3 - An extremely high or extremely low data value is...Ch. 3 - Prob. 23CQCh. 3 - Prob. 24CQCh. 3 - Employee Years of Service In an advertisement, a...Ch. 3 - Newspapers for Sale The average number of...Ch. 3 - Prob. 27CQCh. 3 - Hours Worked The data shown here represent the...Ch. 3 - Prob. 29CQCh. 3 - Prob. 30CQCh. 3 - Exam Scores On a philosophy comprehensive exam,...Ch. 3 - Prob. 32CQCh. 3 - Prob. 1CTCCh. 3 - Ages of U.S. Residents The table shows the median...
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- 2. Which of the following statements are (not) true? lim sup{An U Bn} 818 lim sup{A, B} 818 lim inf{An U Bn} 818 818 lim inf{A, B} An An A, Bn- A, BnB →B = = = lim sup A, U lim sup Bn; 818 818 lim sup A, lim sup Bn; 818 81U lim inf A, U lim inf Bn; 818 818 lim inf A, lim inf Bn; n→X 818 An U BRAUB as no; An OBRANB as n→∞.arrow_forwardThroughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2. 1. Show that AAB (ANB) U (BA) = (AUB) (AB), Α' Δ Β = Α Δ Β, {A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).arrow_forward16. Show that, if X and Y are independent random variables, such that E|X|< ∞, and B is an arbitrary Borel set, then EXI{Y B} = EX P(YE B).arrow_forward
- Proposition 1.1 Suppose that X1, X2,... are random variables. The following quantities are random variables: (a) max{X1, X2) and min(X1, X2); (b) sup, Xn and inf, Xn; (c) lim sup∞ X and lim inf∞ Xn- (d) If Xn(w) converges for (almost) every w as n→ ∞, then lim- random variable. → Xn is aarrow_forwardExercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward
- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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