Introduction To Probability And Statistics
15th Edition
ISBN: 9781337554428
Author: Mendenhall, William.
Publisher: Cengage Learning,
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Chapter 2.3, Problem 17E
To determine
To approximate the value of s using 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 2 Solutions
Introduction To Probability And Statistics
Ch. 2.1 - Measures of CenterFor the data sets in Exercises...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Fortune 500 Revenues Ten of the...Ch. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Calculating the Standard Deviation I For the data...Ch. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - For the data sets in Exercises 79, find the range,...Ch. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Sleep and the College Student A group of 10...Ch. 2.2 - Gas Mileage The miles per gallon (mpg) foreach of...Ch. 2.2 - Polluted Seawater Petroleum pollution in seas...Ch. 2.2 - Prob. 15ECh. 2.3 - Approximating the Standard Deviation For the data...Ch. 2.3 - Approximating the Standard Deviation For the data...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Data Set I A distribution of measurements is...Ch. 2.3 - Prob. 7ECh. 2.3 - Data Set I A distribution of measurements is...Ch. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Data Set II A distribution of measurements has a...Ch. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Breathing Rates Breathing rates for humans canbe...Ch. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - TV Commercials The mean duration of...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - z-ScoresFor the data sets in Exercises 13, find...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - Median and Quartiles For the data in Exercises 46,...Ch. 2.4 - -Number Summary and the Box Plot For each of the...Ch. 2.4 - Five-Number Summary and the Box Plot For each of...Ch. 2.4 - Five-Number Summary and the Box Plot For each of...Ch. 2.4 - Prob. 10ECh. 2.4 - z-Scores vs. Box Plots For the data sets in...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - Percentiles What are the percentiles in Exercises...Ch. 2.4 - For the data in Exercises 1617, find the sample...Ch. 2.4 - For the data in Exercises 1617, find the sample...Ch. 2.4 - €For the data in Exercises 1819, find the...Ch. 2.4 - For the data in Exercises 1819, find the...Ch. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Presidential Vetoes The number of vetoesused by...Ch. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Ages of Pennies Here are the ages of50 pennies,...Ch. 2.4 - Prob. 26ECh. 2 - Raisins The number of raisins in each of...Ch. 2 - Raisins, continued Refer to Exercise 1. a. Find...Ch. 2 - Prob. 3RWYLCh. 2 - Prob. 4RWYLCh. 2 - Prob. 5RWYLCh. 2 - Prob. 6RWYLCh. 2 - Prob. 7RWYLCh. 2 - Prob. 8RWYLCh. 2 - Prob. 9RWYLCh. 2 - Prob. 10RWYLCh. 2 - Prob. 11RWYLCh. 2 - Prob. 12RWYLCh. 2 - Prob. 13RWYLCh. 2 - Prob. 14RWYLCh. 2 - Prob. 15RWYLCh. 2 - Prob. 16RWYLCh. 2 - Prob. 17RWYLCh. 2 - Prob. 18RWYLCh. 2 - Prob. 19RWYLCh. 2 - Prob. 20RWYLCh. 2 - Prob. 21RWYLCh. 2 - Prob. 22RWYLCh. 2 - Prob. 23RWYLCh. 2 - Prob. 24RWYLCh. 2 - Prob. 25RWYL
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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
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