Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Textbook Question

Chapter 2.4, Problem 9E

The proportions of blood phenotypes. A, B, AB, and O, in the population of all Caucasians in the United States are approximately .41, .10, .04, and .45, respectively. A single Caucasian is chosen at random from the population.

a List the sample space for this experiment.
b Make use of the information given above to assign probabilities to each of the simple events.
c What is the probability that the person chosen at random has either type A or type AB blood?

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Chapter 2.3, Problem 8E

Chapter 2.4, Problem 10E

Chapter 2 Solutions

Mathematical Statistics with Applications

Ch. 2.3 - Suppose a family contains two children of...Ch. 2.3 - Suppose that A and B are two events. Write...Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Refer to Exercise 2.4. Use the identities...Ch. 2.3 - Suppose two dice are tossed and the numbers on the...Ch. 2.3 - A group of five applicants for a pair of identical...Ch. 2.3 - From a survey of 60 students attending a...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...

Ch. 2.4 - A sample space consists of five simple events. E1,...Ch. 2.4 - A vehicle arriving at an intersection can turn...Ch. 2.4 - Americans can be quite suspicious, especially when...Ch. 2.4 - A survey classified a large number of adults...Ch. 2.4 - An oil prospecting firm hits oil or gas on 10% of...Ch. 2.4 - Prob. 16E Ch. 2.4 - Hydraulic landing assemblies coming from an...Ch. 2.4 - Suppose two balanced coins are tossed and the...Ch. 2.4 - A business office orders paper supplies from one...Ch. 2.4 - The following game was played on a popular...Ch. 2.4 - If A and B are events, use the result derived in...Ch. 2.4 - If A and B are events and B A, use the result...Ch. 2.4 - Prob. 23E Ch. 2.4 - Use the result in Exercise 2.22 and the Axioms in...Ch. 2.5 - A single car is randomly selected from among all...Ch. 2.5 - According to Websters New Collegiate Dictionary, a...Ch. 2.5 - In Exercise 2.12 we considered a situation where...Ch. 2.5 - Four equally qualified people apply for two...Ch. 2.5 - Two additional jurors are needed to complete a...Ch. 2.5 - Three imported wines are to be ranked from lowest...Ch. 2.5 - A boxcar contains six complex electronic systems....Ch. 2.5 - A retailer sells only two styles of stereo...Ch. 2.5 - The Bureau of the Census reports that the median...Ch. 2.5 - Patients arriving at a hospital outpatient clinic...Ch. 2.6 - An airline has six flights from New York to...Ch. 2.6 - Prob. 36E Ch. 2.6 - A businesswoman in Philadelphia is preparing an...Ch. 2.6 - An upscale restaurant offers a special fixe prix...Ch. 2.6 - An experiment consists of tossing a pair of dice....Ch. 2.6 - A brand of automobile comes in five different...Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - A fleet of nine taxis is to be dispatched to three...Ch. 2.6 - Refer to Exercise 2.43. Assume that taxis are...Ch. 2.6 - Prob. 45E Ch. 2.6 - Ten teams are playing in a basketball tournament....Ch. 2.6 - Refer to Exercise 2.46. If 2n teams are to be...Ch. 2.6 - Prob. 48E Ch. 2.6 - Students attending the University of Florida can...Ch. 2.6 - Prob. 50E Ch. 2.6 - A local fraternity is conducting a raffle where 50...Ch. 2.6 - An experimenter wishes to investigate the effect...Ch. 2.6 - Five firms, F1, F2,, F5, each offer bids on three...Ch. 2.6 - A group of three undergraduate and five graduate...Ch. 2.6 - A study is to be conducted in a hospital to...Ch. 2.6 - A student prepares for an exam by studying a list...Ch. 2.6 - Two cards are drawn from a standard 52-card...Ch. 2.6 - Five cards are dealt from a standard 52-card deck....Ch. 2.6 - Prob. 59E Ch. 2.6 - Refer to Example 2.7. Suppose that we record the...Ch. 2.6 - Prob. 61E Ch. 2.6 - A manufacturer has nine distinct motors in stock,...Ch. 2.6 - The eight-member Human Relations Advisory Board of...Ch. 2.6 - A balanced die is tossed six times, and the number...Ch. 2.6 - Prob. 65E Ch. 2.6 - Refer to Example 2.10. What is the probability...Ch. 2.6 - Refer to Example 2.13. Suppose that the number of...Ch. 2.6 - Show that, for any integer n 1, a (nn)=1....Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.7 - If two events, A and B, are such that P(A) = .5,...Ch. 2.7 - For a certain population of employees, the...Ch. 2.7 - Gregor Mendel was a monk who, in 1865, suggested a...Ch. 2.7 - One hundred adults were interviewed in a telephone...Ch. 2.7 - Prob. 75E Ch. 2.7 - A survey of consumers in a particular community...Ch. 2.7 - A study of the posttreatment behavior of a large...Ch. 2.7 - In the definition of the independence of two...Ch. 2.7 - Suppose that A and B are mutually exclusive...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If P(A) 0, P(B) 0, and P(A) P(A|B), show that...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If A and B are mutually exclusive events and P(B) ...Ch. 2.8 - If A1, A2, and A3 are three events and...Ch. 2.8 - Prob. 85E Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Prob. 89E Ch. 2.8 - Suppose that there is a 1 in 50 chance of injury...Ch. 2.8 - Can A an B be mutually exclusive if P(A) = .4 and...Ch. 2.8 - Prob. 92E Ch. 2.8 - In a game, a participant is given three attempts...Ch. 2.8 - A smoke detector system uses two devices, A and B....Ch. 2.8 - Prob. 95E Ch. 2.8 - If A and B are independent events with P(A) = .5...Ch. 2.8 - Consider the following portion of an electric...Ch. 2.8 - With relays operating as in Exercise 2.97, compare...Ch. 2.8 - Suppose that A and B are independent events such...Ch. 2.8 - Show that Theorem 2.6, the additive law of...Ch. 2.8 - Articles coming through an inspection line are...Ch. 2.8 - Diseases I and II are prevalent among people in a...Ch. 2.8 - Refer to Exercise 2.50. Hours after the rigging of...Ch. 2.8 - If A and B are two events, prove that...Ch. 2.8 - If the probability of injury on each individual...Ch. 2.8 - If A and B are equally likely events and we...Ch. 2.8 - Prob. 107E Ch. 2.8 - If A, B, and C are three events, use two...Ch. 2.8 - Prob. 109E Ch. 2.9 - Of the items produced daily by a factory, 40% come...Ch. 2.9 - Prob. 111E Ch. 2.9 - Three radar sets, operating independently, are set...Ch. 2.9 - Consider one of the radar sets of Exercise 2.112....Ch. 2.9 - A lie detector will show a positive reading...Ch. 2.9 - Prob. 115E Ch. 2.9 - A communications network has a built-in safeguard...Ch. 2.9 - A slate auto-inspection station has two inspection...Ch. 2.9 - Prob. 118E Ch. 2.9 - Suppose that two balanced dice are tossed...Ch. 2.9 - Suppose that two defective refrigerators have been...Ch. 2.9 - Prob. 121E Ch. 2.10 - Applet Exercise Use the applet Bayes Rule as a...Ch. 2.10 - Prob. 123E Ch. 2.10 - A population of voters contains 40% Republicans...Ch. 2.10 - A diagnostic test for a disease is such that it...Ch. 2.10 - Prob. 126E Ch. 2.10 - Prob. 127E Ch. 2.10 - Use Theorem 2.8, the law of total probability, to...Ch. 2.10 - Males and females are observed to react...Ch. 2.10 - A study of Georgia residents suggests that those...Ch. 2.10 - Prob. 131E Ch. 2.10 - A plane is missing and is presumed to have equal...Ch. 2.10 - A student answers a multiple-choice examination...Ch. 2.10 - Two methods, A and B, are available for teaching a...Ch. 2.10 - Of the travelers arriving at a small airport, 60%...Ch. 2.10 - Prob. 136E Ch. 2.10 - Five identical bowls are labeled 1, 2, 3, 4, and...Ch. 2.10 - Prob. 138E Ch. 2.11 - Refer to Exercise 2.112. Let the random variable Y...Ch. 2.11 - Refer to Exercise 2.120. Let the random variable Y...Ch. 2.11 - Refer again to Exercise 2.120. Let the random...Ch. 2.11 - A spinner can land in any of four positions, A, B,...Ch. 2 - Show that Theorem 2.7 holds for conditional...Ch. 2 - Let S contain four sample points, E1, E2, E3, and...Ch. 2 - Prob. 145SE Ch. 2 - Prob. 146SE Ch. 2 - Prob. 147SE Ch. 2 - A bin contains three components from supplier A,...Ch. 2 - A large group of people is to be checked for two...Ch. 2 - 2.149 A large group of people is to be checked for...Ch. 2 - Prob. 151SE Ch. 2 - Prob. 152SE Ch. 2 - Prob. 153SE Ch. 2 - a A drawer contains n = 5 different and...Ch. 2 - A group of men possesses the three characteristics...Ch. 2 - The accompanying table lists accidental deaths by...Ch. 2 - Prob. 157SE Ch. 2 - A bowl contains w white balls and b black balls....Ch. 2 - Prob. 159SE Ch. 2 - A machine for producing a new experimental...Ch. 2 - Prob. 161SE Ch. 2 - Prob. 162SE Ch. 2 - Relays used in the construction of electric...Ch. 2 - Prob. 164SE Ch. 2 - Refer to Exercise 2.163 and consider circuit B. If...Ch. 2 - Prob. 166SE Ch. 2 - Prob. 167SE Ch. 2 - As in Exercises 2.166 and 2.167, eight tires of...Ch. 2 - Three beer drinkers (say I, II, and III) are to...Ch. 2 - Prob. 170SE Ch. 2 - Prob. 171SE Ch. 2 - Prob. 172SE Ch. 2 - Prob. 173SE Ch. 2 - Prob. 174SE Ch. 2 - Prob. 175SE Ch. 2 - Prob. 176SE Ch. 2 - Refer to Exercise 2.90(b) where a friend claimed...Ch. 2 - Suppose that the probability of exposure to the...Ch. 2 - Two gamblers bet 1 each on the successive tosses...Ch. 2 - Prob. 180SE Ch. 2 - Suppose that n indistinguishable balls are to be...

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Solution Summary: The author lists the sample space for the given experiment. The set of all possible sample points of the experiment can be termed as sampling space.

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