Probability And Statistical Inference (10th Edition)

10th Edition

ISBN: 9780135189399

Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Publisher: PEARSON

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Textbook Question

Chapter 1.4, Problem 19E

Extend Example 1.4-6 to an n-sided die. That is, suppose that a fair n-sided die is rolled ii independent times. A match occurs if side us observed on the ith trial, i = 1,2,. .. n.

(a) Show that the probability of at least one match is 1 − ( n − 1 n ) n = 1 − ( n − 1 n ) n .

(b) Find the limit of this probability as n increases without bound.

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Chapter 1.4, Problem 18E

Chapter 1.4, Problem 20E

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Read the scenario and decide which (if any) of the assumptions or conditions for using the Central Limit Theorem are violated. An appliance manufacturer stockpiles washers and dryers in a large warehouse. They currently have over 2500 washers and dryers in their inventory. Their goal is that no more than 2% of all appliances are damaged in storage. An inspector randomly selects 200 washers in its inventory and finds that 8 of them are damaged. Are any conditions violated? Group of answer choices Violates the Independent / Randomization condition (i.e. the sample is not random). Violates the Big Population condition (i.e. the population is not big enough) Violates the Large Sample condition (i.e. the sample is not large enough). Does not violate any condition or assumption.

Which of the following is NOT a condition that ALWAYS has to be satisfied to apply the Central Limit Theorem to the sample mean? a) The sample size must be larger than 30 b) There are no obvious outliers in the sample if the sample size is less than 30 c) There are no extreme outliers in the sample if the sample size is at least 30. d) The sample observations are independent.

Which of the following statements about the Central Limit Theorem (CLT) is correct?1. The CLT states that the sample mean is always equal to the population mean.2. The CLT states that the sampling distribution of the sample mean is approximately normal for large sample sizes (n > 30).3. The CLT states that the sample mean is equal to the population mean, provided that n > 30.4. The CLT states that the sampling distribution of the population mean is approximately normal, provided that n > 30. In a distribution plot, if the mean is equal to the median, is the possible shape of the distribution skewed to the right, skewed to the left, or symmetric? If batteries have lives that are normally distribute with mean 2, 800 hours and standard deviation 400 hours, using the 68-95-99.7 rule to approximate the percentage of batteries having a life less than 3, 600 hours.

Chapter 1 Solutions

Probability And Statistical Inference (10th Edition)

Ch. 1.1 - Of a group of patients having injuries, 28% visit...Ch. 1.1 - An insurance company looks at its auto insurance...Ch. 1.1 - Draw one card at random from a standard deck of...Ch. 1.1 - A fair coin is tossed four times, and the sequence...Ch. 1.1 - Consider the trial on which a 3 is first observed...Ch. 1.1 - If P(A)=0.5,P(B)=0.6, and P(AB)=0.4, find (a)...Ch. 1.1 - Given that P(AB)=0.76 and P(AB)=0.87, find P(A).Ch. 1.1 - During a visit to a primary care physicians...Ch. 1.1 - Roll a fair six-sided die three times. Let...Ch. 1.1 - Prove Theorem 1.1-6.

Ch. 1.1 - A typical roulette wheel used in a casino has 38...Ch. 1.1 - Let x equal a number that is selected randomly...Ch. 1.1 - Divide a line segment into two parts by selecting...Ch. 1.1 - Let the interval [r,r] be the base of a...Ch. 1.1 - Let S=A1A2...Am, where events A1,A2,...,Am are...Ch. 1.1 - Let pn,n=0,1,2..., be the probability that an...Ch. 1.2 - A combination lock was left at a fitness center....Ch. 1.2 - In designing an experiment, the researcher can...Ch. 1.2 - How many different license plates are possible if...Ch. 1.2 - The eating club is hosting a make-your-own sun-dae...Ch. 1.2 - How many four-letter code words are possible using...Ch. 1.2 - Suppose that Novak Djokovic and Roger Federer are...Ch. 1.2 - In a state lottery, four digits are drawn at...Ch. 1.2 - How many different varieties of pizza can be made...Ch. 1.2 - The World Series in baseball continues until...Ch. 1.2 - Pascals triangle gives a method for calculating...Ch. 1.2 - Three students (S) and six faculty members (F) are...Ch. 1.2 - Prove: r=0n(1)r(nr)=0andr=0n(nr)=2n HINT: Consider...Ch. 1.2 - A bridge hand is found by taking 13 cards at...Ch. 1.2 - At the end of a semester, 29 students in a...Ch. 1.2 - Prove Equation 1.2-2. HINT: First selectn1...Ch. 1.2 - A box of candy hearts contains 52 hearts, of which...Ch. 1.2 - A poker hand is defined as drawing five cards at...Ch. 1.2 - For each positive integer n, let P({n})=(12)n....Ch. 1.3 - A common screening test for 1-IIV is called the...Ch. 1.3 - The following table classifies 1456 people by...Ch. 1.3 - Let A1 and A2 be the events that a person is left-...Ch. 1.3 - Two cards are drawn successively and without...Ch. 1.3 - Suppose that the gene for eye color for a certain...Ch. 1.3 - A researcher finds that, of 982 men who died in...Ch. 1.3 - An urn contains four colored halls: two orange and...Ch. 1.3 - An urn contains 17 balls marked LOSE and three...Ch. 1.3 - An urn contains four balls numbered 1 through 4....Ch. 1.3 - A single card is drawn at random from each of six...Ch. 1.3 - Consider the birthdays of the students in a class...Ch. 1.3 - You are a member of a class of 18 students. A bowl...Ch. 1.3 - In the gambling game craps. two dice are rolled...Ch. 1.3 - Some albatrosses return to the worlds only...Ch. 1.3 - An urn contains eight red and seven blue balls. A...Ch. 1.3 - Bowl A contains three red and two white chips, and...Ch. 1.4 - Let A and B be independent events with P(A)=0.7...Ch. 1.4 - Let P(A)=0.3 and P(B)=0.6. (a) Find P(AB) when A...Ch. 1.4 - Let A and B be independent events with P(A)=14 and...Ch. 1.4 - Prove parts (b) and (c) of Theorem 1.4-1.Ch. 1.4 - If P(A)=0.8,P(B)=0.5, and P(AB)=0.9, are A and B...Ch. 1.4 - Show that if A, B, and C are mutually independent,...Ch. 1.4 - Each of three football players will attempt to...Ch. 1.4 - Die A has orange on one face and blue on five...Ch. 1.4 - Suppose that A, B, and C are mutually independent...Ch. 1.4 - Let D1,D2,D3 be three four-sided dice whose sides...Ch. 1.4 - Let A and B be two events. (a) If the events A and...Ch. 1.4 - Flip an unbiased coin five independent times....Ch. 1.4 - An urn contains two red balls and four white...Ch. 1.4 - In Example 1.4-5, suppose that the probability of...Ch. 1.4 - An urn contains ten red and ten white balls. The...Ch. 1.4 - An urn contains five balls, one marked WIN and...Ch. 1.4 - Each of the 12 students in a class is given a fair...Ch. 1.4 - An eight-team single-elimination tournament is set...Ch. 1.4 - Extend Example 1.4-6 to an n-sided die. That is,...Ch. 1.4 - Hunters A and B shoot at a target with...Ch. 1.4 - There are eight major blood types, whose...Ch. 1.5 - Bowl B1 contains two white chips, bowl B2 contains...Ch. 1.5 - Bean seeds from supplier A have an 85% germination...Ch. 1.5 - A doctor is concerned about the relationship...Ch. 1.5 - Assume that an insurance company knows the...Ch. 1.5 - At a hospitals emergency room, patients are...Ch. 1.5 - A life insurance company issues standard,...Ch. 1.5 - A chemist wishes to detect an impurity in a...Ch. 1.5 - A store sells four brands of tablets. The least...Ch. 1.5 - There is a new diagnostic test for a disease that...Ch. 1.5 - Prob. 10E Ch. 1.5 - At the beginning of a certain study of a group of...Ch. 1.5 - Two processes of a company produce rolls of...Ch. 1.5 - A hospital receives 40% of its flu vaccine from...

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Solution Summary: The author explains the multiplicative rule for any two independent events AandB, which is defined by: P(A_i)=1n

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Chapter 1 Solutions