Introduction To Probability And Statistics
15th Edition
ISBN: 9781337554428
Author: Mendenhall, William.
Publisher: Cengage Learning,
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Chapter 4.5, Problem 15E
Screening Tests Suppose that a certain diseaseis present in 10% of the population, and that there is ascreening test designed to detect this disease if present.The test does not always work perfectly. Sometimesthe test is negative when the disease is present, andsometimes it is positive when the disease is absent. Thefollowing table shows the proportion of times that thetest produces various results.
a. Find the following probabilities from the table:
b. Use Bayes’ Rule and the results of part a to find
c. Use the definition of conditional
d. Find the probability of a false positive, thatthe test is positive, given that the person isdisease-free.
e. Find the probability of a false negative, that thetest is negative, given that the person has thedisease.
f. Are either of the probabilities in parts d or e largeenough that you would be concerned about the reliabilityof this screening method? Explain.
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9.2 Testing the Mean mu:
Problem 3
(1 point)
Test the claim that the population of sophomore college
students has a mean grade point average greater than 2.2.
Sample statistics include n = 71, x = 2.44, and s = 0.9.
Use a significance level of a = 0.01.
The test statistic is
The P-Value is between :
The final conclusion is
< P-value <
A. There is sufficient evidence to support the claim that
the mean grade point average is greater than 2.2.
○ B. There is not sufficient evidence to support the claim
that the mean grade point average is greater than 2.2.
Note: You can earn partial credit on this problem.
Note: You are in the Reduced Scoring Period. All work counts for
50% of the original.
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Chapter 4 Solutions
Introduction To Probability And Statistics
Ch. 4.1 - Experiment I A single die is tossed. List the...Ch. 4.1 - Experiment I A single die is tossed. List the...Ch. 4.1 - Experiment I A single die is tossed. List the...Ch. 4.1 - Experiment I A single die is tossed. List the...Ch. 4.1 - Experiment I A single die is tossed. List the...Ch. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Experiment II A sample space contains seven...Ch. 4.1 - Prob. 9ECh. 4.1 - Experiment II A sample space contains seven...
Ch. 4.1 - Prob. 11ECh. 4.1 - Experiment II A sample space contains seven...Ch. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Simple Events Define the simple events for...Ch. 4.1 - Simple Events Define the simple events for...Ch. 4.1 - Prob. 19ECh. 4.1 - Simple Events Define the simple events for...Ch. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Tree Diagrams Use a tree diagram to find the...Ch. 4.1 - Table of Outcomes Use a table of outcomes to...Ch. 4.1 - Table of Outcomes Use a table of outcomes to...Ch. 4.1 - Table of Outcomes Use a table of outcomes to...Ch. 4.1 - The Urn Problem A bowl contains three red and two...Ch. 4.1 - Prob. 29ECh. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment I A single fair die is tossed....Ch. 4.2 - Experiment II A sample space contains seven...Ch. 4.2 - Experiment II A sample space contains seven...Ch. 4.2 - Experiment II A sample space contains seven...Ch. 4.2 - Experiment II A sample space contains seven...Ch. 4.2 - Experiment III A sample space consists of five...Ch. 4.2 - Experiment III A sample space consists of five...Ch. 4.2 - Experiment III A sample space consists of five...Ch. 4.2 - Experiment III A sample space consists of five...Ch. 4.2 - Experiment III A sample space consists of five...Ch. 4.2 - Prob. 16ECh. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Spaces and Probability For the experiments in...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Sample Spaces and Probability For the experiments...Ch. 4.2 - Free Throws A particular basketball player hits70%...Ch. 4.2 - Four Coins A jar contains four coins: a nickel,a...Ch. 4.2 - Preschool or Not? A teacher randomly selects 1...Ch. 4.2 - Need Eyeglasses? A large number of adults...Ch. 4.2 - Prob. 31ECh. 4.2 - Aspirin Refer to Exercise 31 and find...Ch. 4.2 - Jury Duty Three people are randomly selected...Ch. 4.2 - Jury Duty II Refer to Exercise 33. Suppose...Ch. 4.2 - Tea Tasters A single person is hired to taste...Ch. 4.2 - -Meter Run Four equally qualified runners,John,...Ch. 4.2 - Fruit Flies In a genetics experiment, the...Ch. 4.2 - Playing the Slots A slot machine has three...Ch. 4.2 - Pepsi™ or Coke™? An experiment is conducted ata...Ch. 4.2 - Flextime A survey to determine the availability...Ch. 4.3 - The mn Rule Use the mn Rule to find the number...Ch. 4.3 - The mn Rule Use the mn Rule to find the number of...Ch. 4.3 - The mn Rule Use the mn Rule to find the number of...Ch. 4.3 - The mn Rule Use the mn Rule to find the number of...Ch. 4.3 - Permutations Evaluate the permutations inExercises...Ch. 4.3 - Permutations Evaluate the permutations in...Ch. 4.3 - Permutations Evaluate the permutations in...Ch. 4.3 - Permutations Evaluate the permutations in...Ch. 4.3 - Combinations Evaluate the combinations inExercises...Ch. 4.3 - Combinations Evaluate the combinations in...Ch. 4.3 - Combinations Evaluate the combinations in...Ch. 4.3 - Combinations Evaluate the combinations in...Ch. 4.3 - Choosing People In how many ways can youselect...Ch. 4.3 - Choosing People, again In how many ways canyou...Ch. 4.3 - The Urn Problem, again Three balls are...Ch. 4.3 - What to Wear? You own 4 pairs of jeans, 12...Ch. 4.3 - Itineraries A businessman in New York is...Ch. 4.3 - Vacation Plans Your family vacation involves...Ch. 4.3 - A Card Game Three students are playing a cardgame....Ch. 4.3 - Dinner at Gerard’s A French restaurant offers...Ch. 4.3 - Playing Poker Five cards are selected from...Ch. 4.3 - Poker II Refer to Exercise 21. You have a...Ch. 4.3 - A Hospital Survey A study is to be conducted in...Ch. 4.3 - Traffic Problems Two city council members are tobe...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Cramming A student prepares for an exam bystudying...Ch. 4.3 - Monkey Business A monkey is given 12 blocks:3...Ch. 4.3 - Viruses A certain virus afflicted the families...Ch. 4.4 - Experiment I An experiment can result in one of...Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Experiment I An experiment can result in one of...Ch. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Experiment II Suppose P(A)=.1andP(B)=.5.Answer the...Ch. 4.4 - Experiment II Suppose P(A)=.1and P(B)=.5. Answer...Ch. 4.4 - Experiment II Suppose P(A)=.1and P(B)=.5. Answer...Ch. 4.4 - Experiment II Suppose P(A)=.1and P(B)=.5. Answer...Ch. 4.4 - Experiment III An experiment can result in one...Ch. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Dice An experiment consists of tossing a single...Ch. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Drug Testing In testing prospective employees...Ch. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Starbucks or Peet’s®? A college student frequents...Ch. 4.4 - Prob. 30ECh. 4.4 - Smoking and Cancer A survey of people in a...Ch. 4.4 - Smoke Detectors A smoke-detector system usestwo...Ch. 4.4 - Plant Genetics In 1865, Gregor Mendel suggesteda...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Choosing a Mate Men and women often disagreeon how...Ch. 4.4 - Jordan and Durant Two stars of the LA Clippersand...Ch. 4.5 - Bayes’ Rule I A sample is selected from one of two...Ch. 4.5 - Bayes’ Rule I A sample is selected from one of two...Ch. 4.5 - Bayes’ Rule I A sample is selected from one of two...Ch. 4.5 - Bayes’ Rule II When an experiment is conducted,...Ch. 4.5 - Bayes’ Rule II When an experiment is conducted,...Ch. 4.5 - Bayes’ Rule II When an experiment is conducted,...Ch. 4.5 - Law of Total Probability A population can...Ch. 4.5 - Violent Crime City crime records show that 20%...Ch. 4.5 - Worker Error A worker-operated machine producesa...Ch. 4.5 - Airport Security Suppose that, in a particular...Ch. 4.5 - Prob. 11ECh. 4.5 - No Pass, No Play Under the “no pass, no play”rule...Ch. 4.5 - Medical Diagnostics Different illnesses can...Ch. 4.5 - Cheating on Your Taxes? Suppose 5% of all...Ch. 4.5 - Screening Tests Suppose that a certain diseaseis...Ch. 4 - Whistle Blowers Although there is legal...Ch. 4 - DVRs A retailer sells two styles of digital...Ch. 4 - Prob. 3RWYLCh. 4 - A Reticent Salesman The probability that a...Ch. 4 - Prob. 5RWYLCh. 4 - Prob. 6RWYLCh. 4 - Prob. 7RWYLCh. 4 - Prob. 8RWYLCh. 4 - Prob. 9RWYLCh. 4 - Prob. 10RWYLCh. 4 - Prob. 11RWYLCh. 4 - The Match Game Two men each toss a coin....Ch. 4 - Contract Negotiations Experience has shown...Ch. 4 - Prob. 14RWYLCh. 4 - Prob. 15RWYLCh. 4 - Prob. 16RWYLCh. 4 - Mass Transit Only 40% of all people in a...Ch. 4 - Prob. 18RWYLCh. 4 - Prob. 19RWYLCh. 4 - Prob. 20RWYLCh. 4 - Prob. 21RWYL
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