Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134679259
Author: Bennett
Publisher: PEARSON
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Textbook Question
Chapter 6.3, Problem 21E
Psychology of Expected Values. In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. Here are two scenarios that he used, each of which required people to choose between two options.
Decision 1
Option A: 100% chance of gaining $1,000,000
Option B: 10% chance of gaining $2,500,000; 89% chance of gaining $1,000,000; and 1% chance of gaining nothing
Decision 2
Option A: 11% chance of gaining $1,000,000 and 89% chance of gaining nothing
Option B: 10% chance of gaining $2,500,000 and 90% chance of gaining nothing
Allais discovered that for Decision 1, most people chose Option A, while for Decision 2, most people chose Option B.
- a. For each decision, find the expected value of each option.
- b. Are the responses given in the survey consistent with the expected values?
- c. Give a possible explanation for the responses in Allais’s survey.
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Check out a sample textbook solutionStudents have asked these similar questions
1. It's often said that "you should only invest as much money as you can afford to lose." Do you agree with this statement? Why or why not?
2. Risk Aversion is a measure of how much a person dislikes taking risks, especially with investment. If you were on a game show and the host
offered you a choice between taking $1000 and leaving, or risking everything to try to win $5000, what would you choose? How would you
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Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences
property damage in the next five years, the company must pay out $23,600 to the policy holder. Executives at Avicenna are considering offering these policies
for $791 each. Suppose that for each holder of a policy there is a 3% chance they will experience property damage in the next five years and a 97% chance
they will not.
(If necessary, consult a list of formulas.)
If the executives at Avicenna know that they will sell many of these policies, should they expect
to make or lose money from offering them? How much?
To answer, take into account the price of the policy and the expected value of the amount paid
out to the holder.
O Avicenna can expect to make money from offering these policies.
In the long run, they should expect to make
dollars on each policy sold.
O Avicenna can expect to lose money from offering these policies.…
A management is faced with the problem of choosing one of three products
for manufacturing. The potential demand for each product may turn out to be good,
moderate or poor. The probabilities for each of the state of nature wère estimated as
follows :
Nature of Demand
Product
Good
Moderate
Poor
0.7
0.2
0.1
Y
0.5
0.3
0.2
0.4.
0.5
0.1
The estimated profit or loss under the three states may be taken as :
30,000
20,000
10,000
Y
60,000
30,000
20,000
40,000
10,000
- 15,000 (loss)
Prepare the expected value table and advise the management about the choice of product.
Chapter 6 Solutions
Statistical Reasoning for Everyday Life (5th Edition)
Ch. 6.1 - Coin Tossing. Suppose you toss a coin 100 times....Ch. 6.1 - Statistical Significance. What do we mean when we...Ch. 6.1 - Prob. 3ECh. 6.1 - Quantifying Significance. What does it mean to say...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...
Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Prob. 17ECh. 6.1 - Carpal Tunnel Syndrome Treatments. An experiment...Ch. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Human Body Temperature. In a study by researchers...Ch. 6.1 - Seat Belts and Children. In a study of children...Ch. 6.1 - Prob. 23ECh. 6.1 - Subjective Significance. For each event in...Ch. 6.2 - Outcomes and Events. Distinguish between an...Ch. 6.2 - Notation. What does it mean when we write P(A)?...Ch. 6.2 - Probability Types. Briefly describe the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Does It Make Sense? For Exercises 58, determine...Ch. 6.2 - Prob. 7ECh. 6.2 - Does It Make Sense? For Exercises 58, determine...Ch. 6.2 - Counting Outcomes. How many different three-child...Ch. 6.2 - Prob. 10ECh. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Days of the Week. What is the probability of...Ch. 6.2 - Days of the Week. What is the probability of...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Prob. 38ECh. 6.2 - Probability Distributions. In Exercises 39 and 40,...Ch. 6.2 - Probability Distributions. In Exercises 39 and 40,...Ch. 6.3 - Law of Large Numbers. What is the law of large...Ch. 6.3 - Understanding the Law of Large Numbers. In terms...Ch. 6.3 - Expected Value. What is an expected value, and how...Ch. 6.3 - Gamblers Fallacy. What is the gamblers fallacy?...Ch. 6.3 - Prob. 5ECh. 6.3 - Does It Make Sense? For Exercises 58, determine...Ch. 6.3 - Prob. 7ECh. 6.3 - Does It Make Sense? For Exercises 58, determine...Ch. 6.3 - Gender Selection. In analyzing genders of...Ch. 6.3 - Speedy Driver. A person who has a habit of driving...Ch. 6.3 - Should You Play? Suppose you are offered this...Ch. 6.3 - Kentuckys Pick 4 Lottery. If you bet 1 in...Ch. 6.3 - Expected Value for Life Insurance. There is a...Ch. 6.3 - Expected Value for Life Insurance There is a...Ch. 6.3 - Expected Waiting Time. You arrive at a bus stop...Ch. 6.3 - Expected Value in Roulette. As shown in Figure...Ch. 6.3 - Expected Value in Casino Dice. When you give a...Ch. 6.3 - New Jersey Pick 4. In New Jerseys Pick 4 lottery,...Ch. 6.3 - Extra Points in Football. Football teams have the...Ch. 6.3 - Prob. 20ECh. 6.3 - Psychology of Expected Values. In 1953, a French...Ch. 6.3 - Behind in Coin Tossing: Can You Catch Up? Suppose...Ch. 6.4 - Risk and Travel. What is travel risk? Give an...Ch. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Does It Make Sense? For Exercises 58, determine...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Commercial Aviation. For Exercises 912, use the...Ch. 6.4 - Commercial Aviation. For Exercises 912, use the...Ch. 6.4 - Prob. 12ECh. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Vital Statistics. For Exercises 1720, use the data...Ch. 6.4 - Vital Statistics. 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The game of BINGO involves drawing numbered...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - The Binary Computer Company manufactures computer...Ch. 6 - For a recent year, the fatality rate from motor...Ch. 6 - A Las Vegas handicapper can correctly predict the...Ch. 6 - For the handicapper in Exercise 1, find the...Ch. 6 - In a clinical trial of the effectiveness of a...Ch. 6 - If P(A) = 0.65, what is the value of P(not A)?Ch. 6 - In Exercises 610, use the following results. The...Ch. 6 - In Exercises 610, use the following results. The...Ch. 6 - Prob. 8CQCh. 6 - In Exercises 610, use the following results. The...Ch. 6 - In Exercises 610, use the following results. The...
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