Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305750999
Author: Peck Olson Devore
Publisher: CENGAGE C
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Textbook Question
Chapter 6.5, Problem 43E
Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the
- a. Give a relative frequency interpretation of the given probability.
- b. What is the probability that a call is not for medical assistance?
- c. Assuming that successive calls are independent of one another, calculate the probability that two successive calls will both be for medical assistance. (Hint: See Example 6.18.)
- d. Still assuming independence, calculate the probability that for two successive calls, the first is for medical assistance and the second is not for medical assistance.
- e. Still assuming independence, calculate the probability that exactly one of the next two calls will be for medical assistance. (Hint: There are two different possibilities. The one call for medical assistance might be the first call, or it might be the second call.)
- f. Do you think that it is reasonable to assume that the requests made in successive calls are independent? Explain.
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9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
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2,3,
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28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
Chapter 6 Solutions
Introduction to Statistics and Data Analysis
Ch. 6.1 - Define the term chance experiment, and give an...Ch. 6.1 - Define the term sample space, and then give the...Ch. 6.1 - Consider the chance experiment in which the type...Ch. 6.1 - A tennis shop sells five different brands of...Ch. 6.1 - A new model of laptop computer can be ordered with...Ch. 6.1 - A college library has four copies of a certain...Ch. 6.1 - A library has five copies of a certain textbook on...Ch. 6.1 - Suppose that, starting at a certain time,...Ch. 6.1 - Refer to the previous exercise and now suppose...Ch. 6.1 - Prob. 10E
Ch. 6.1 - An engineering construction firm is currently...Ch. 6.1 - Consider a Venn diagram picturing two events A and...Ch. 6.3 - A large department store offers online ordering....Ch. 6.3 - The manager of a music store has kept records of...Ch. 6.3 - A bookstore sells two types of books (fiction and...Ch. 6.3 - ▼ Medical insurance status—covered (C) or not...Ch. 6.3 - Roulette is a game of chance that involves...Ch. 6.3 - Phoenix is a hub for a large airline. Suppose that...Ch. 6.3 - A professor assigns five problems to be completed...Ch. 6.3 - Refer to the following information on full-term...Ch. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - A deck of 52 playing cards is mixed well, and 5...Ch. 6.3 - Prob. 26ECh. 6.3 - The student council for a school of science and...Ch. 6.3 - A student placement center has requests from five...Ch. 6.3 - Prob. 29ECh. 6.4 - Two different airlines have a flight from Los...Ch. 6.4 - The article Chances Are You Know Someone with a...Ch. 6.4 - The accompanying data are from the article...Ch. 6.4 - The following graphical display is similar to one...Ch. 6.4 - Delayed diagnosis of cancer is a problem because...Ch. 6.4 - The events E and T are defined as E = the event...Ch. 6.4 - The newspaper article Folic Acid Might Reduce Risk...Ch. 6.4 - Suppose that an individual is randomly selected...Ch. 6.4 - Is ultrasound a reliable method for determining...Ch. 6.4 - The table at the top of the next page summarizes...Ch. 6.4 - USA Today (June 6, 2000) gave information on seal...Ch. 6.4 - Prob. 41ECh. 6.4 - The paper Good for Women, Good for Men, Bad for...Ch. 6.5 - Many fire stations handle emergency calls for...Ch. 6.5 - The paper Predictors of Complementary Therapy Use...Ch. 6.5 - The report TV Drama/Comedy Viewers and Health...Ch. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - In a small city, approximately 15% of those...Ch. 6.5 - Jeanie is a bit forgetful, and if she doesnt make...Ch. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - The following case study was reported in the...Ch. 6.5 - Three friends (A, B, and C) will participate in a...Ch. 6.5 - Prob. 55ECh. 6.5 - A store sells two different brands of dishwasher...Ch. 6.5 - The National Public Radio show Car Talk used to...Ch. 6.5 - Refer to the previous exercise. Suppose now that...Ch. 6.6 - A university has 10 vehicles available for use by...Ch. 6.6 - Prob. 60ECh. 6.6 - Prob. 61ECh. 6.6 - Let F denote the event that a randomly selected...Ch. 6.6 - According to a July 31, 2013 posting on cnn.com, a...Ch. 6.6 - Suppose that Blue Cab operates 15% of the taxis in...Ch. 6.6 - A large cable company reports the following: 80%...Ch. 6.6 - Refer to the information given in the previous...Ch. 6.6 - The authors of the paper Do Physicians Know When...Ch. 6.6 - A study of how people are using online services...Ch. 6.6 - Prob. 69ECh. 6.6 - Prob. 70ECh. 6.6 - Prob. 71ECh. 6.6 - Prob. 72ECh. 6.6 - Prob. 73ECh. 6.6 - The paper referenced in the previous exercise also...Ch. 6.6 - In an article that appears on the web site of the...Ch. 6.6 - Prob. 76ECh. 6.6 - Only 0.1% of the individuals in a certain...Ch. 6.7 - The Los Angeles Times (June 14, 1995) reported...Ch. 6.7 - Five hundred first-year students at a state...Ch. 6.7 - The table given below describes (approximately)...Ch. 6.7 - On April 1, 2010, the Bureau of the Census in the...Ch. 6 - A company uses three different assembly linesA1,...Ch. 6 - Prob. 88CRCh. 6 - Prob. 89CRCh. 6 - Prob. 90CRCh. 6 - Prob. 91CRCh. 6 - A company sends 40% of its overnight mail parcels...Ch. 6 - Prob. 93CRCh. 6 - Prob. 94CRCh. 6 - In a school machine shop, 60% of all machine...Ch. 6 - There are five faculty members in a certain...Ch. 6 - The general addition rule for three events states...Ch. 6 - A theater complex is currently showing four...Ch. 6 - Prob. 100CRCh. 6 - Suppose that a box contains 25 light bulbs, of...Ch. 6 - Prob. 102CRCh. 6 - A transmitter is sending a message using a binary...
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- 27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward
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