Statistics (13th Edition)
13th Edition
ISBN: 9780134080215
Author: James T. McClave, Terry T Sincich
Publisher: PEARSON
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Chapter 4.3, Problem 40UP
To determine
Explain what the
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Twenty-eight applicants interested in working for the Food Stamp program took an examination designed
to measure their aptitude for social work. A stem-and-leaf plot of the 28 scores appears below, where the
first column is the count per branch, the second column is the stem value, and the remaining digits are the
leaves.
a) List all the values.
Count
1
Stems
Leaves
4
6
1
4
6
567
9
3688
026799
9
8
145667788
7
9
1234788
b) Calculate the first quartile (Q1) and the third Quartile (Q3).
c) Calculate the interquartile range.
d) Construct a boxplot for this data.
Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Chapter 4 Solutions
Statistics (13th Edition)
Ch. 4.1 - What is a random variable?
Ch. 4.1 - How do discrete and continuous random variables...Ch. 4.1 - Type of Random Variable. Classify the following...Ch. 4.1 - Type of Random Variable. Identify the following...Ch. 4.1 - Type of Random Variable. Identify the following...Ch. 4.1 - 4.3 NHTSA crash tests. Refer to the National...Ch. 4.1 - 4.4 Customers in line at a Subway shop. The number...Ch. 4.1 - Sound waves from a basketball. Refer to the...Ch. 4.1 - Mongolian desert ants. Refer to the Journal of...Ch. 4.1 - Motivation of drug dealers. Refer to the Applied...
Ch. 4.1 - Psychology. Give an example of a discrete random...Ch. 4.1 - Sociology. Give an example of a discrete random...Ch. 4.1 - Nursing. Give an example of a discrete random...Ch. 4.1 - Art history. Give an example of a discrete random...Ch. 4.1 - Irrelevant speech effects. Refer to the Acoustical...Ch. 4.1 - Shaft graves in ancient Greece. Refer to the...Ch. 4.2 - Give three different ways of representing the...Ch. 4.2 - Consider the following probability...Ch. 4.2 - 4.11 A discrete random variable x can assume five...Ch. 4.2 - Explain why each of the following is or is not a...Ch. 4.2 - The random variable x has the following discrete...Ch. 4.2 - The random variable x has the discrete probability...Ch. 4.2 - 4.16 Toss three fair coins and let x equal the...Ch. 4.2 - Use the applet entitled Random Numbers to generate...Ch. 4.2 - Run the applet entitled Simulating the Probability...Ch. 4.2 - Size of TV households. According to Nielsen’s...Ch. 4.2 - 4.25 Do social robots walk or roll? Refer to the...Ch. 4.2 - NHTSA crash tests. Refer to the National Highway...Ch. 4.2 - Downloading apps to your cell phone. According to...Ch. 4.2 - Controlling the water hyacinth. An insect that...Ch. 4.2 - Gender in two-child families. Human Biology (Feb....Ch. 4.2 - Environmental vulnerability of amphibians. Many...Ch. 4.2 - The “last name” effect in purchasing. The Journal...Ch. 4.2 - Solar energy cells. According to the Earth Policy...Ch. 4.2 - 4.29 Contaminated gun cartridges. A weapons...Ch. 4.2 - Prob. 34ACICh. 4.2 - Prob. 35ACICh. 4.2 - Reliability of a manufacturing network. A team of...Ch. 4.2 - 4.38 Voter preferences for a committee. A...Ch. 4.2 - Prob. 38ACACh. 4.2 - Robot-sensor system configuration. Engineers at...Ch. 4.3 - What does the expected value of a random variable...Ch. 4.3 - Will E(x) always be equal to a specific value of...Ch. 4.3 - For a mound-shaped, symmetric distribution, what...Ch. 4.3 - Consider the probability distribution for the...Ch. 4.3 - 4.18 Consider the probability distribution for the...Ch. 4.3 - Consider the probability distributions shown...Ch. 4.3 - 4.17 Consider the probability distribution...Ch. 4.3 - NHTSA car crash tests. Refer to Exercise 4.26 (p....Ch. 4.3 - Downloading apps to your cell phone. Refer to the...Ch. 4.3 - Controlling the water hyacinth. Refer to the...Ch. 4.3 - Gender in two-child families. Refer to the Human...Ch. 4.3 - Environmental vulnerability of amphibians. Refer...Ch. 4.3 - Reliability of a manufacturing network. Refer to...Ch. 4.3 -
Beach erosional hot spots. Refer to the U.S....Ch. 4.3 - 4.36 Expected Lotto winnings. Most states offer...Ch. 4.3 -
Expected winnings in roulette. In the popular...Ch. 4.3 - 4.39 Parlay card betting. Odds makers try to...Ch. 4.4 - Give the five characteristics of a binomial random...Ch. 4.4 - Give the formula for p(x) for a binomial random...Ch. 4.4 - Consider the following binomial probability...Ch. 4.4 - Refer to Exercise 4.59.
Graph the probability...Ch. 4.4 - 4.40 Compute the following:
Ch. 4.4 - 4.42 Suppose x is a binomial random variable with...Ch. 4.4 - 4.43 If x is a binomial random variable, compute p...Ch. 4.4 - If x is a binomial random variable, use Table I in...Ch. 4.4 - If x is a binomial random variable, use Table I in...Ch. 4.4 - 4.45 If x is a binomial random variable, calculate...Ch. 4.4 - 4.46 The binomial probability distribution is a...Ch. 4.4 - Applet Exercise 4.3
Use the applets Simulating the...Ch. 4.4 - Applet Exercise 4.4
Open the applet Sample from a...Ch. 4.4 - Prob. 4.5AECh. 4.4 - Working on summer vacation. An Adweek/Harris (July...Ch. 4.4 - Superstitions survey. Are Americans superstitious?...Ch. 4.4 - Where will you get your next pet? According to an...Ch. 4.4 - Chemical signals of mice. Refer to the Cell (May...Ch. 4.4 - Analysis of bottled water. Is the bottled water...Ch. 4.4 - Caesarian births. The American College of...Ch. 4.4 - 4.53 Fingerprint expertise. Refer to the...Ch. 4.4 - Hotel guest satisfaction. J. D. Power and...Ch. 4.4 - 4.52 Immediate feedback to incorrect exam answers....Ch. 4.4 - 4.54 Making your vote count. Refer to the Chance...Ch. 4.4 - Prob. 78ACICh. 4.4 - Victims of domestic abuse. According to...Ch. 4.4 - Prob. 80ACICh. 4.4 - Testing a psychic’s ESP. Refer to Exercise 3.101...Ch. 4.4 - Assigning a passing grade. A literature professor...Ch. 4.4 - Prob. 83ACACh. 4.4 - Does having boys run in the family? Chance (Fall...Ch. 4.5 - Give the four characteristics of a Poisson random...Ch. 4.5 - Consider a Poisson random variable with...Ch. 4.5 - Consider the Poisson probability distribution...Ch. 4.5 - Refer to Exercise 4.86.
Graph the probability...Ch. 4.5 - Refer to Exercise 4.87.
Graph the probability...Ch. 4.5 - 4.65 Given that x is a random variable for which a...Ch. 4.5 - Assume that x is a random variable having a...Ch. 4.5 - Suppose x is a random variable for which a Poisson...Ch. 4.5 - Suppose x is a random variable for which a Poisson...Ch. 4.5 - As mentioned in this section, when n is large, p...Ch. 4.5 - Eye fixation experiment. Cognitive scientists at...Ch. 4.5 - Noise in laser imaging. Penumbrol imaging is a...Ch. 4.5 - Spare line replacement units. The U.S. Department...Ch. 4.5 - 4.176 NASA and rare planet transits. A “planet...Ch. 4.5 - 4.71 Airline fatalities. Over the past 5 years,...Ch. 4.5 - 4.76 Traffic fatalities and sporting events. The...Ch. 4.5 - LAN videoconferencing. A network administrator is...Ch. 4.5 - 4.80 Making high-stakes insurance decisions. The...Ch. 4.5 - Davy Crockett’s use of words. Davy Crockett, a...Ch. 4.5 - 4.79 Flaws in plastic-coated wire. The British...Ch. 4.5 - 4.82 Waiting for a car wash. An automatic car wash...Ch. 4.5 - 4.83 Elevator passenger arrivals. A study of the...Ch. 4.6 - Explain the difference between sampling with...Ch. 4.6 - Give the characteristics of a hypergeometric...Ch. 4.6 - How do binomial and hypergeometric random...Ch. 4.6 - 4.64 Given that x is a hypergeometric random...Ch. 4.6 - 4.63 Given that x is a hypergeometric random...Ch. 4.6 - Prob. 112LMCh. 4.6 - Prob. 113LMCh. 4.6 - 4.68 Given that x is a hypergeometric random...Ch. 4.6 - 4.67 Suppose you plan to sample 10 items from a...Ch. 4.6 - 4.69 Do social robots walk or roll? Refer to the...Ch. 4.6 - Mail rooms contaminated with anthrax. In Chance...Ch. 4.6 - Prob. 118ACBCh. 4.6 - 4.183 On-site treatment of hazardous waste. The...Ch. 4.6 - 4.78 Guilt in decision making. The Journal of...Ch. 4.6 - 4.73 Contaminated gun cartridges. Refer to the...Ch. 4.6 - Lot inspection sampling. Imagine that you are...Ch. 4.6 - Prob. 123ACICh. 4.6 - Prob. 124ACICh. 4.6 - Establishing boundaries in academic engineering....Ch. 4.6 - Prob. 126ACACh. 4.6 - Awarding of home improvement grants. The...Ch. 4 - Prob. 128UPCh. 4 - 4.161 Identify the type of random...Ch. 4 - 4.156 For each of the following examples, decide...Ch. 4 - Prob. 131LMCh. 4 - Prob. 132LMCh. 4 - Prob. 133LMCh. 4 - Prob. 134LMCh. 4 - Prob. 135LMCh. 4 - Prob. 136ACBCh. 4 - Prob. 137ACBCh. 4 - Prob. 138ACBCh. 4 - Prob. 139ACBCh. 4 - Prob. 140ACBCh. 4 - Prob. 141ACBCh. 4 - Prob. 142ACBCh. 4 - Prob. 143ACBCh. 4 - Prob. 144ACBCh. 4 - Prob. 145ACBCh. 4 - Prob. 146ACICh. 4 - Extinct New Zealand birds. Refer to the...Ch. 4 - Student gambling on sports. A study of gambling...Ch. 4 - Parents’ behavior at a gym meet. Pediatric...Ch. 4 - 4.196 Testing for spoiled wine. Suppose that you...Ch. 4 - Prob. 151ACICh. 4 - Prob. 152ACICh. 4 - Chickens with fecal contamination. The United...Ch. 4 - Crime Watch neighborhood. In many cities,...Ch. 4 - 4.203 The showcase showdown. On the popular...Ch. 4 - 4.60 Network forensic analysis. A network forensic...Ch. 4 - 4.201 How many questionnaires to mail? The...Ch. 4 - 4.204 Reliability of a “one-shot” device. A...Ch. 4 - Emergency room bed availability. The mean number...Ch. 4 - Prob. 160CTC
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- Theorem 2.6 (The Minkowski inequality) Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and E|Y P <00. Then X+YpX+Yparrow_forwardTheorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and set Var X = 0². Then, for 0 0, P(X > x) ≤e-x+1²² P(|X|>x) ≤2e-1x+1²² (ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for x > 0. and 0x) ≤2 exp Σ k=1 (iii) If, in addition, X1, X2, X, are identically distributed, then P(S|x) ≤2 expl-tx+nt²o).arrow_forwardTheorem 5.1 (Jensen's inequality) state without proof the Jensen's Ineg. Let X be a random variable, g a convex function, and suppose that X and g(X) are integrable. Then g(EX) < Eg(X).arrow_forward
- Can social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 76% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events. (Round your answers to three decimal places.) answer parts a-c. a) Out of 30 job listings, at least 19 will conduct social media screening. b) Out of 30 job listings, fewer than 17 will conduct social media screening. c) Out of 30 job listings, exactly between 19 and 22 (including 19 and 22) will conduct social media screening. show all steps for probabilities please. answer parts a-c.arrow_forwardQuestion: we know that for rt. (x+ys s ا. 13. rs. and my so using this, show that it vye and EIXI, EIYO This : E (IX + Y) ≤2" (EIX (" + Ely!")arrow_forwardTheorem 2.4 (The Hölder inequality) Let p+q=1. If E|X|P < ∞ and E|Y| < ∞, then . |EXY ≤ E|XY|||X|| ||||qarrow_forward
- Theorem 7.6 (Etemadi's inequality) Let X1, X2, X, be independent random variables. Then, for all x > 0, P(max |S|>3x) ≤3 max P(S| > x). Isk≤narrow_forwardTheorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).If the chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forwardTheorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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