Essentials of Statistics, Books a la Carte Edition (6th Edition)
6th Edition
ISBN: 9780134687131
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 4, Problem 1FDD
Critical Thinking: Interpreting results from a test for smoking
It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse CO-oximeters may be a way to get information about smoking without relying on patients’ statements. Pulse CO-oximeters use Light that shines through a fingernail, and it measures carbon monoxide in blood. These devices are used by firemen and emergency departments to detect carbon monoxide poisoning, but they can also be used to identify smokers. The accompanying table lists results from people aged 18–44 when the pulse CO-oximeter is set to detect a 6% or higher level of carboxyhemoglobin (based on data from “Carbon Monoxide Test Can Be Used to Identify Smoker.” by Patrice Wendling. Internal Medicine News, Vol. 40., No. 1, and Centers for Disease Control and Prevention).
CO-Oximetry Test for Smoking
Analyzing the Results
1. False Positive Based on the results in the table, find the
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
7. Cantelli's inequality. Let X be a random variable with finite variance, o².
(a) Prove that, for x ≥ 0,
P(X EX2x)≤
02
x² +0²
202
P(|X - EX2x)<≤
(b) Find X assuming two values where there is equality.
(c) When is Cantelli's inequality better than Chebyshev's inequality?
(d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall,
from Proposition 6.1, that an application of Chebyshev's inequality yields
the bound o√√2.
(e) Generalize Cantelli's inequality to moments of order r 1.
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.
Chapter 4 Solutions
Essentials of Statistics, Books a la Carte Edition (6th Edition)
Ch. 4.1 - New Jersey Lottery Let A denote the event of...Ch. 4.1 - Probability Rewrite the following statement so...Ch. 4.1 - Interpreting Weather While this exercise was being...Ch. 4.1 - Subjective Probability Estimate the probability...Ch. 4.1 - Identifying Probability Values Which of the...Ch. 4.1 - Penicillin Who discovered penicillin: Sean Penn,...Ch. 4.1 - Avogadro Constant If you are asked on a quiz to...Ch. 4.1 - Births Example 2 in this section includes the...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...
Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 9-12, assume that 50 births are...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - SAT Test When making a random guess for an answer...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - Randomness When using a computer to randomly...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 13-20, express the indicated degree...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 21-24, refer to the sample data in...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - In Exercises 25-32, find the probability and...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Probability from a Sample Space. In Exercises...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Using Probability to Form Conclusions. In...Ch. 4.1 - Kentucky Pick 4 In the Kentucky Pick 4 lottery,...Ch. 4.1 - Finding Odds in Roulette A roulette wheel has 38...Ch. 4.1 - Kentucky Derby Odds When the horse California...Ch. 4.1 - Relative Risk and Odds Ratio In a clinical trial...Ch. 4.2 - Notation When randomly selecting an adult, A...Ch. 4.2 - Notation When randomly selecting adults, let M...Ch. 4.2 - Sample for a Poll There are 15,524,971 adults in...Ch. 4.2 - Rule of Complements When randomly selecting an...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - Finding Complements. In Exercises 5-8, find the...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20; use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 9-20, use the data in the following...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - In Exercises 21-24, use these results from the...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Redundancy. Exercises 25 and 26 involve...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - Acceptance Sampling. With one method of a...Ch. 4.2 - In Exercises 29 and 30, find the probabilities and...Ch. 4.2 - Prob. 30BSCCh. 4.2 - Surge Protectors Refer to the accompanying figure...Ch. 4.2 - Prob. 32BBCh. 4.2 - Exclusive Or The exclusive or means either one or...Ch. 4.2 - Complements and the Addition Rule Refer to the...Ch. 4.3 - Language: Complement of At Least One Let A = the...Ch. 4.3 - Probability of At Least One Let A = the event of...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - Notation When selecting one of your Facebook...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Probability of a Girl Assuming that boys and girls...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - At Least One. In Exercises 5-12, find the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - Denomination Effect. In Exercises 13-16, use the...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - In Exercises 17-20, refer to the accompanying...Ch. 4.3 - Redundancy in Computer Hard Drives Assume that...Ch. 4.3 - Redundancy in Stadium Generators Large stadiums...Ch. 4.3 - Composite Drug Test Based on the data in Table 4-1...Ch. 4.3 - Composite Water Samples The Fairfield County...Ch. 4.3 - Shared Birthdays Find the probability that of 25...Ch. 4.4 - Notation What does the symbol ! represent? Six...Ch. 4.4 - New Jersey Pick 6 In the New Jersey Pick 6 lottery...Ch. 4.4 - Oregon Pick 4 In the Oregon Pick 4 lottery game, a...Ch. 4.4 - Combination Lock The typical combination lock uses...Ch. 4.4 - In Exercises 536, express all probabilities as...Ch. 4.4 - Social Security Numbers A Social Security number...Ch. 4.4 - Quinela In a horse race, a quinela bet is won if...Ch. 4.4 - Soccer Shootout In soccer, a tie at the end of...Ch. 4.4 - Grading Exams Your professor has just collected...Ch. 4.4 - Radio Station Call Letters If radio station call...Ch. 4.4 - Scheduling Routes A presidential candidate plans...Ch. 4.4 - Survey Reliability A survey with 12 questions is...Ch. 4.4 - Safety with Numbers The author owns a safe in...Ch. 4.4 - Electricity When testing for current in a cable...Ch. 4.4 - Sorting Hat At Hogwarts School of Witchcraft and...Ch. 4.4 - Moving Company The United Van Lines moving company...Ch. 4.4 - Powerball As of this writing, the Powerball...Ch. 4.4 - Teed Off When four golfers are about to begin a...Ch. 4.4 - ZIP Code If you randomly select five digits, each...Ch. 4.4 - FedEx Deliveries With a short time remaining in...Ch. 4.4 - Phone Numbers Current rules for telephone area...Ch. 4.4 - Classic Counting Problem A classic counting...Ch. 4.4 - Corporate Officers and Committees The Digital Pet...Ch. 4.4 - ATM You want to obtain cash by using an ATM, but...Ch. 4.4 - Party Mix DJ Marty T is hosting a party tonight...Ch. 4.4 - Identity Theft with Credit Cards Credit card...Ch. 4.4 - What a Word! One of the longest words in standard...Ch. 4.4 - Phase I of a Clinical Trial A clinical test on...Ch. 4.4 - Mega Millions As of this writing, the Mega...Ch. 4.4 - Designing Experiment Clinical trials of Nasonex...Ch. 4.4 - Morse Codes The International Morse code is a way...Ch. 4.4 - Mendels Peas Mendel conducted some his famous...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Counting with Fingers How many different ways can...Ch. 4.4 - Change for a Quarter How many different ways can...Ch. 4.4 - Win 1 Billion Quicken Loans offered a prize of 1...Ch. 4.4 - Computer Variable Names A common computer...Ch. 4.4 - High Fives a. Five mathletes celebrate after...Ch. 4 - Standard Tests Standard tests, such as the SAT or...Ch. 4 - Rain As the author is creating this exercise, a...Ch. 4 - Months If a month is randomly selected after...Ch. 4 - Social Networking Based on data from the Pew...Ch. 4 - Subjective Probability Estimate the probability...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 610, use the following results from...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - In Exercises 110, use the data in the accompanying...Ch. 4 - Prob. 10RECh. 4 - Black Cars Use subjective probability to estimate...Ch. 4 - Vision Correction About 75% of the U.S. population...Ch. 4 - National Statistics Day a. If a person is randomly...Ch. 4 - Composite Sampling for Diabetes Currently, the...Ch. 4 - Wild Card Lottery The Wild Card lottery is run in...Ch. 4 - Pennsylvania Cash 5 In the Pennsylvania Cash 5...Ch. 4 - Redundancy Using Braun battery-powered alarm...Ch. 4 - Exacta In a horse race, an exacta bet is won by...Ch. 4 - Fatal Drunk Driving Listed below are the blood...Ch. 4 - Fatal Drunk Driving Use the same data given in...Ch. 4 - Organ Donors USA Today provided information about...Ch. 4 - Sampling Eye Color Based on a study by Dr. P....Ch. 4 - Prob. 5CRECh. 4 - New Lottery Game In the Monopoly Millionaires Club...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...Ch. 4 - Critical Thinking: Interpreting results from a...
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