ELEMENTARY STATISTICS: STEP BY STEP- ALE
10th Edition
ISBN: 9781266422362
Author: Bluman
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Chapter 14.1, Problem 8E
List the advantages and disadvantages of systematic sampling.
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
7. Cantelli's inequality. Let X be a random variable with finite variance, o².
(a) Prove that, for x ≥ 0,
P(X EX2x)≤
02
x² +0²
202
P(|X - EX2x)<≤
(b) Find X assuming two values where there is equality.
(c) When is Cantelli's inequality better than Chebyshev's inequality?
(d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall,
from Proposition 6.1, that an application of Chebyshev's inequality yields
the bound o√√2.
(e) Generalize Cantelli's inequality to moments of order r 1.
The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.
Chapter 14 Solutions
ELEMENTARY STATISTICS: STEP BY STEP- ALE
Ch. 14.1 - The White or Wheat Bread Debate Read the following...Ch. 14.1 - Name the four basic sampling techniques.Ch. 14.1 - Why are samples used in statistics?Ch. 14.1 - What is the basic requirement for a sample?Ch. 14.1 - Why should random numbers be used when you are...Ch. 14.1 - List three incorrect methods that are often used...Ch. 14.1 - What is the principle behind random numbers?Ch. 14.1 - List the advantages and disadvantages of random...Ch. 14.1 - List the advantages and disadvantages of...Ch. 14.1 - List the advantages and disadvantages of...
Ch. 14.1 - List the advantages and disadvantages of cluster...Ch. 14.1 - Teacher Data Using the table of random numbers,...Ch. 14.1 - Prob. 12ECh. 14.1 - Teacher Data Select a cluster sample of 10 states,...Ch. 14.1 - Record High Temperatures Which method of sampling...Ch. 14.1 - Prob. 16ECh. 14.1 - Electoral Votes Select a systematic sample of 10...Ch. 14.1 - Electoral Votes Divide the 50 states into five...Ch. 14.1 - Prob. 19ECh. 14.1 - Define sampling or selection bias.Ch. 14.1 - Prob. 22ECh. 14.1 - Define nonresponsive bias.Ch. 14.1 - Prob. 24ECh. 14.1 - Define response or interview bias.Ch. 14.1 - Prob. 26ECh. 14.1 - Define volunteer bias.Ch. 14.1 - Give an example of how volunteer bias might occur.Ch. 14.2 - Prob. 1ACCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 11ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.3 - Simulations Answer the following questions: 1....Ch. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Who is responsible for the development of modern...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14 - Hurricanes Select a random sample of eight storms...Ch. 14 - Prob. 14.1.2RECh. 14 - Hurricanes Select a cluster of 10 storms. Compute...Ch. 14 - Prob. 14.1.4RECh. 14 - Prob. 14.1.5RECh. 14 - Prob. 14.1.6RECh. 14 - Prob. 14.1.8RECh. 14 - Prob. 14.2.9RECh. 14 - Prob. 14.2.10RECh. 14 - Prob. 14.2.11RECh. 14 - Prob. 14.2.12RECh. 14 - Prob. 1DACh. 14 - Prob. 2DACh. 14 - Select a cluster sample of 20 individuals, and...Ch. 14 - Prob. 4DACh. 14 - Prob. 5DACh. 14 - Determine whether each statement is true or false....Ch. 14 - Prob. 2CQCh. 14 - Prob. 3CQCh. 14 - Prob. 4CQCh. 14 - Prob. 5CQCh. 14 - Prob. 6CQCh. 14 - Interviewing selected people at a local...Ch. 14 - Prob. 8CQCh. 14 - Prob. 9CQCh. 14 - Prob. 10CQCh. 14 - Blood Pressure Select a random sample of 12...Ch. 14 - Prob. 12CQCh. 14 - Blood Pressure Divide the individuals into...Ch. 14 - Prob. 14CQCh. 14 - Prob. 25CQCh. 14 - Prob. 26CQCh. 14 - Prob. 27CQCh. 14 - Prob. 28CQCh. 14 - For Exercises 2530, explain why the survey...Ch. 14 - Prob. 30CQCh. 14 - Prob. 1DP
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- The Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardWhat was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forward
- What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forwardThere are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.arrow_forwardshow all stepsarrow_forward
- Most people know that the probability of getting a head when you flip a fair coin is . You want to use the relative frequency of the event to show that the probability is . How many times should you simulate flipping the coin in the experiment? Would it be better to use 300 trials or 3000 trials? Explain.arrow_forwardThe qualified applicant pool for eight management trainee positions consists of ten women and six men. How many different groups of applicants can be selected for the positionsarrow_forwardYou want to make a salad from whatever vegetable you have in the fridge. You have seven different tomatoes. There are 2 red tomatoes, 4 yellow tomatoes, and one black tomato in the fridge. You have three different bell peppers. There is 1 red pepper, 1 yellow pepper, and 1 green pepper. What is the probability of randomly choosing a vegetable and getting a red tomato, and a green pepper? Round your answer to four decimal places.arrow_forward
- uppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state offers the lowest premium? Which state offers the highest premium?arrow_forwardWing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 58% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 86% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(B|Ac). Round your answer to the nearest hundredth.arrow_forwardYou draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. If you get a3on the first card, find the probability of drawing a 3 for the second card.arrow_forward
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