EBK ESSENTIALS OF STATISTICS FOR BUSINE
8th Edition
ISBN: 8220103648783
Author: Anderson
Publisher: CENGAGE L
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Chapter 3, Problem 71SE
a.
To determine
Draw a
Check whether there is any relationship between the two variables.
b.
To determine
Find the sample
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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 3 Solutions
EBK ESSENTIALS OF STATISTICS FOR BUSINE
Ch. 3.1 - Consider a sample with data values of 10, 20, 12,...Ch. 3.1 - Consider a sample with data values of 10, 20, 21,...Ch. 3.1 - Consider the following data and corresponding...Ch. 3.1 - Consider the following data.
What is the mean...Ch. 3.1 - Consider a sample with data values of 27, 25, 20,...Ch. 3.1 - Consider a sample with data values of 53, 55, 70,...Ch. 3.1 - The average number of minutes Americans commute to...Ch. 3.1 - Prob. 8ECh. 3.1 - Advertising Spending. Which companies spend the...Ch. 3.1 - Over a nine-month period, OutdoorGearLab tested...
Ch. 3.1 - According to the National Education Association...Ch. 3.1 - The Big Bang Theory, a situation comedy featuring...Ch. 3.1 - Automobile Fuel Efficiencies. In automobile...Ch. 3.1 - The data contained in the file named StateUnemp...Ch. 3.1 - Motor Oil Prices. Martinez Auto Supplies has...Ch. 3.1 - Calculating Grade Point Averages. The grade point...Ch. 3.1 - The following table shows the total return and the...Ch. 3.1 - Business School Ranking. Based on a survey of...Ch. 3.1 - Annual revenue for Corning Supplies grew by 5.5%...Ch. 3.1 - Prob. 20ECh. 3.1 - If an asset declines in value from $5000 to $3500...Ch. 3.1 - The current value of a company is 25 million. If...Ch. 3.2 - Consider a sample with data values of 10, 20, 12,...Ch. 3.2 - Consider a sample with data values of 10, 20, 12,...Ch. 3.2 - Consider a sample with data values of 27, 25, 20,...Ch. 3.2 - Price of Unleaded Gasoline. Data collected by the...Ch. 3.2 - The results of a search to find the least...Ch. 3.2 - The Australian Open is the first of the four Grand...Ch. 3.2 - Air Quality Index. The Los Angeles Times regularly...Ch. 3.2 - Prob. 30ECh. 3.2 - The results of Accounting Principals’ latest...Ch. 3.2 - Advertising Spend by Companies. Advertising Age...Ch. 3.2 - Scores turned in by an amateur golfer at the...Ch. 3.2 - Consistency of Running Times. The following times...Ch. 3.3 - Consider a sample with data values of 10, 20, 12,...Ch. 3.3 - Prob. 36ECh. 3.3 - Consider a sample with a mean of 30 and a standard...Ch. 3.3 - Suppose the data have a bell-shaped distribution...Ch. 3.3 - The results of a national survey showed that on...Ch. 3.3 - The Energy Information Administration reported...Ch. 3.3 - GMAT Exam Scores. The Graduate Management...Ch. 3.3 - Many families in California are using backyard...Ch. 3.3 - Prob. 43ECh. 3.3 - NCAA Basketball Game Scores. A sample of 10 NCAA...Ch. 3.3 - Prob. 45ECh. 3.4 - Consider a sample with data values of 27, 25, 20,...Ch. 3.4 - Show the boxplot for the data in exercise 46. 46....Ch. 3.4 - Prob. 48ECh. 3.4 - Prob. 49ECh. 3.4 - Naples Half-Marathon Times. Naples, Florida, hosts...Ch. 3.4 - Annual sales, in millions of dollars, for 21...Ch. 3.4 - Cell Phone Companies Customer Satisfaction....Ch. 3.4 - Most Admired Companies. Fortune magazines list of...Ch. 3.4 - U.S. Border Crossings. The Bureau of...Ch. 3.5 - Five observations taken for two variables follow....Ch. 3.5 - Five observations taken for two variables follow....Ch. 3.5 - Ten major college football bowl games were played...Ch. 3.5 - Driving Speed and Fuel Efficiency. A department of...Ch. 3.5 - Smoke Detector Use and Death Rates. Over the past...Ch. 3.5 - Stock Market Indexes Comparison. The Russell 1000...Ch. 3.5 - Best Private Colleges. A random sample of 30...Ch. 3 - Prob. 62SECh. 3 - USA Today reports that NCAA colleges and...Ch. 3 - Physician Office Waiting Times. The average...Ch. 3 - Worker Productivity and Insomnia. U.S. companies...Ch. 3 - A study of smartphone users shows that 68% of...Ch. 3 - Prob. 67SECh. 3 - Prob. 68SECh. 3 - Prob. 69SECh. 3 - Best Hotels. Travel + Leisure magazine provides an...Ch. 3 - Prob. 71SECh. 3 - MLB Team Winning Percentages. Does a major league...Ch. 3 - Money Market Funds Days to Maturity. The days to...Ch. 3 - Automobile Speeds. Automobiles traveling on a road...Ch. 3 - Annual Returns for Panama Railroad Company Stock....Ch. 3 - Pelican Stores, a division of National Clothing,...Ch. 3 - The motion picture industry is a competitive...Ch. 3 - The pursuit of a higher education degree in...Ch. 3 - Although millions of elephants once roamed across...
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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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