Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 2.9, Problem 118E
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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. 3ECh. 2.3 - Prob. 4ECh. 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. 16ECh. 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. 23ECh. 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. 36ECh. 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. 41ECh. 2.6 - Prob. 42ECh. 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. 45ECh. 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. 48ECh. 2.6 - Students attending the University of Florida can...Ch. 2.6 - Prob. 50ECh. 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. 59ECh. 2.6 - Refer to Example 2.7. Suppose that we record the...Ch. 2.6 - Prob. 61ECh. 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. 65ECh. 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. 69ECh. 2.6 - Prob. 70ECh. 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. 75ECh. 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. 85ECh. 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. 89ECh. 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. 92ECh. 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. 95ECh. 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. 107ECh. 2.8 - If A, B, and C are three events, use two...Ch. 2.8 - Prob. 109ECh. 2.9 - Of the items produced daily by a factory, 40% come...Ch. 2.9 - Prob. 111ECh. 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. 115ECh. 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. 118ECh. 2.9 - Suppose that two balanced dice are tossed...Ch. 2.9 - Suppose that two defective refrigerators have been...Ch. 2.9 - Prob. 121ECh. 2.10 - Applet Exercise Use the applet Bayes Rule as a...Ch. 2.10 - Prob. 123ECh. 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. 126ECh. 2.10 - Prob. 127ECh. 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. 131ECh. 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. 136ECh. 2.10 - Five identical bowls are labeled 1, 2, 3, 4, and...Ch. 2.10 - Prob. 138ECh. 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. 145SECh. 2 - Prob. 146SECh. 2 - Prob. 147SECh. 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. 151SECh. 2 - Prob. 152SECh. 2 - Prob. 153SECh. 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. 157SECh. 2 - A bowl contains w white balls and b black balls....Ch. 2 - Prob. 159SECh. 2 - A machine for producing a new experimental...Ch. 2 - Prob. 161SECh. 2 - Prob. 162SECh. 2 - Relays used in the construction of electric...Ch. 2 - Prob. 164SECh. 2 - Refer to Exercise 2.163 and consider circuit B. If...Ch. 2 - Prob. 166SECh. 2 - Prob. 167SECh. 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. 170SECh. 2 - Prob. 171SECh. 2 - Prob. 172SECh. 2 - Prob. 173SECh. 2 - Prob. 174SECh. 2 - Prob. 175SECh. 2 - Prob. 176SECh. 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. 180SECh. 2 - Suppose that n indistinguishable balls are to be...
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- Suppose that you take a sample of 100 from a population that contains 45 percent Democrats. What sample size condition do you need to check here (if any)?What’s the standard error of ^P?Compare the standard errors of ^p n=100 for ,n=1000 , n=10,000, and comment.arrow_forwardSuppose that a class’s test scores have a mean of 80 and standard deviation of 5. You choose 25 students from the class. What’s the chance that the group’s average test score is more than 82?arrow_forwardSuppose that you collect data on 10 products and check their weights. The average should be 10 ounces, but your sample mean is 9 ounces with standard deviation 2 ounces. Find the standard score.What percentile is the standard score found in part a of this question closest to?Suppose that the mean really is 10 ounces. Do you find these results unusual? Use probabilities to explain.arrow_forward
- Suppose that you want to sample expensive computer chips, but you can have only n=3 of them. Should you continue the experiment?arrow_forwardSuppose that studies claim that 40 percent of cellphone owners use their phones in the car while driving. What’s the chance that more than 425 out of a random sample of 1,000 cellphone owners say they use their phones while driving?arrow_forwardSuppose that the average length of stay in Europe for American tourists is 17 days, with standard deviation 4.5. You choose a random sample of 16 American tourists. The sample of 16 stay an average of 18.5 days or more. What’s the chance of that happening?arrow_forward
- How do you recognize that a statistical problem requires you to use the CLT? Think of one or two clues you can look for. (Assume quantitative data.)arrow_forwardSuppose that you take a sample of 100 from a skewed population with mean 50 and standard deviation 15. What sample size condition do you need to check here (if any)?What’s the shape and center of the sampling distribution for ?What’s the standard error?arrow_forwardQuestion 3 The following stem-and-leaf displays the weekly salary of employees at this firm. Stem-and-Leaf Display Leaf Unit = 10.0 N=x 5 3 00123 12 4 0125888 (y) 5 11234456777 z 6 13568 5 7 154 2 8 46 i. Determine the value of x, y and z. [3] ii. What is the value of the median? [2] iii. Find the mode of this data set. iv. Calculate the range [1] [2]arrow_forward
- Let Y be a continuous RV with PDF otherwise Find the CDF, Fry), of Y . Find an expression for pth, p € (0, 1), quantile of the distribution. Find E(Y) and V(Y). Find E(-2Y + 1) and V(-3Y - 2). Find E(Y3).arrow_forwardLet X be a continuous RV with CDF Find P(X < 0), P(-1 < X < 1) and P(0.5 < X). Based on your answers to the above questions, what is the median of the distribu-tion? Why Find the PDF, fx (x), of X.arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward
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