Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Chapter 10, Problem 80CR
An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers were selected and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per gallon) are:
Assuming that fuel efficiency is
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For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
blank
c. What is the probability that a…
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.
Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 10 Solutions
Introduction to Statistics and Data Analysis
Ch. 10.1 - Explain why the statement x=50 is not a legitimate...Ch. 10.1 - For the following pairs, indicate which do not...Ch. 10.1 - To determine whether the pipe welds in a nuclear...Ch. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - A researcher speculates that because of...Ch. 10.1 - A county commissioner must vote on a resolution...Ch. 10.1 - A cruise ship charges passengers 3 for a can of...
Ch. 10.1 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Medical personnel are required to report suspected...Ch. 10.2 - Prob. 15ECh. 10.2 - A television manufacturer claims that (at least)...Ch. 10.2 - A manufacturer of hand-held calculators receives...Ch. 10.2 - Water specimens are taken from water used for...Ch. 10.2 - Suppose that for a particular hypothesis test, the...Ch. 10.2 - Suppose that you arc an inspector for the Fish and...Ch. 10.2 - Prob. 21ECh. 10.2 - An automobile manufacturer is considering using...Ch. 10.3 - Use the definition of the P-value to explain the...Ch. 10.3 - For which of the following P-values will the null...Ch. 10.3 - Prob. 25ECh. 10.3 - Let p denote the proportion of students at a...Ch. 10.3 - Assuming a random sample from a large population,...Ch. 10.3 - Prob. 28ECh. 10.3 - In a survey of 1000 women age 22 to 35 who work...Ch. 10.3 - The paper Debt Literacy, Financial Experiences and...Ch. 10.3 - "Most Like it Hot" is the title of a press release...Ch. 10.3 - In a survey of 1005 adult Americans, 46% indicated...Ch. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - The article Cops Get Screened for Digital Dirt...Ch. 10.3 - Refer back to the previous exercise. The actual...Ch. 10.3 - The report 2007 Electronic Monitoring ...Ch. 10.3 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Give as much information as you can about the...Ch. 10.4 - Paint used to paint lines on roads must reflect...Ch. 10.4 - A certain pen has been designed so that actual...Ch. 10.4 - Prob. 46ECh. 10.4 - The paper Playing Active Video Games Increases...Ch. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Medical research has shown that repeated wrist...Ch. 10.4 - Prob. 53ECh. 10.4 - A comprehensive study conducted by the National...Ch. 10.4 - Prob. 55ECh. 10.4 - The paper titled Music for Pain Relief (The...Ch. 10.4 - Many consumers pay careful attention to stated...Ch. 10.4 - Much concern has been expressed regarding the...Ch. 10.5 - The power of a test is influenced by the sample...Ch. 10.5 - Prob. 60ECh. 10.5 - Let denote the mean lifetime (in hours) for a...Ch. 10.5 - The city council in a large city has become...Ch. 10.5 - The amount of shaft wear after a fixed mileage was...Ch. 10.5 - Optical fibers are used in telecommunications to...Ch. 10.5 - Prob. 65ECh. 10.6 - In 2006, Boston Scientific sought approval for a...Ch. 10.6 - The article Boy or Girl: Which Gender Baby Would...Ch. 10 - Prob. 68CRCh. 10 - In a national survey of 2013 adults, 1590...Ch. 10 - Students at the Akademia Podlaka conducted an...Ch. 10 - Prob. 71CRCh. 10 - Prob. 72CRCh. 10 - A number of initiatives on the topic of legalized...Ch. 10 - Prob. 74CRCh. 10 - Prob. 75CRCh. 10 - Prob. 76CRCh. 10 - Prob. 77CRCh. 10 - Duck hunting in populated areas faces opposition...Ch. 10 - Past experience has indicated that the response...Ch. 10 - An automobile manufacturer who wishes to advertise...Ch. 10 - A student organization uses the proceeds from a...Ch. 10 - A hot tub manufacturer advertises that with its...Ch. 10 - Prob. 1CRECh. 10 - Prob. 2CRECh. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - Prob. 5CRECh. 10 - The article Should Canada Allow Direct-to-Consumer...Ch. 10 - Prob. 7CRECh. 10 - It probably wouldnt surprise you to know that...Ch. 10 - The article Doctors Cite Burnout in Mistakes (San...Ch. 10 - The National Geographic Society conducted a study...Ch. 10 - Heinz Plays Catch-up After Under-Filling Ketchup...Ch. 10 - In a survey conducted by Yahoo Small Business,...Ch. 10 - In an AP-AOL sports poll (Associated Press,...Ch. 10 - Prob. 14CRECh. 10 - A survey of teenagers and parents in Canada...Ch. 10 - The same survey referenced in the previous...
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- In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 4 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardIn Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 2 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1 2 3 4 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forward
- A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. x f(x) for x = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(x) ≥0 Σf(x) = 1 (5.1) (5.2) Does this probability distribution satisfy equation (5.1)? Select Does this probability distribution satisfy equation (5.2)? Select b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardWest Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. Excel File: data05-19.xls 10 20 f(x) .05 .10 11 30 40 50 60 .10 .20 .35 .20 a. Is this probability distribution valid? Yes Explain. greater than or equal to 0 f(x) Σf(x) equal to 1 b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)? c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)? d. Compute the expected value and variance of x. Expected value Variance clients per year squared clients per yeararrow_forward
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