Statistical Techniques in Business and Economics
18th Edition
ISBN: 9781260579611
Author: Douglas Lind; William Marchal; Samuel Wathen
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 19, Problem 2E
Out of 110 diesel engines tested, a rework and repair facility found 9 had leaky water pumps, 15 had faulty cylinders, 4 had ignition problems, 52 had oil leaks, and 30 had cracked blocks. Draw a Pareto chart to identify the key problem in the engines.
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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 19 Solutions
Statistical Techniques in Business and Economics
Ch. 19 - The Rouse Home, located on the south side of...Ch. 19 - Tom Sharkey is the owner of Sharkey Chevy, Buick,...Ch. 19 - Out of 110 diesel engines tested, a rework and...Ch. 19 - The manager of River City McDonalds randomly...Ch. 19 - Describe the difference between assignable...Ch. 19 - Describe the difference between an attribute...Ch. 19 - Samples of size n = 4 are selected from a...Ch. 19 - Samples of size 5 are selected from a...Ch. 19 - A new industrial oven has just been installed at...Ch. 19 - Refer to Exercise 7. a. On the basis of this...
Ch. 19 - Auto-Lite Company manufactures car batteries. At...Ch. 19 - Below is a p-chart for a manufacturing process. a....Ch. 19 - Inter-State Moving and Storage Company is setting...Ch. 19 - A bicycle manufacturer randomly selects 10 frames...Ch. 19 - During the process of producing toilet paper,...Ch. 19 - Sams Supermarkets monitors the checkout scanners...Ch. 19 - Dave Christi runs a car wash chain with outlets...Ch. 19 - Compute the probability of accepting a lot of DVDs...Ch. 19 - Determine the probability of accepting lots that...Ch. 19 - Determine the probability of accepting lots that...Ch. 19 - Warren Electric manufactures fuses for many...Ch. 19 - Grills Video Products purchases LCDs from Mira...Ch. 19 - The production supervisor at Westburg Electric...Ch. 19 - The manufacturer of running shoes conducted a...Ch. 19 - At Rumseys Old Fashion Roast Beef, cola drinks are...Ch. 19 - A new machine has just been installed to produce...Ch. 19 - Long Last Tire Company, as part of its inspection...Ch. 19 - Charter National Bank has a staff of loan officers...Ch. 19 - Prob. 25CECh. 19 - Early Morning Delivery Service guarantees delivery...Ch. 19 - An automatic machine produces 5.0-millimeter bolts...Ch. 19 - Steele Breakfast Foods Inc. produces a popular...Ch. 19 - An investor believes there is a 5050 chance that a...Ch. 19 - Lahey Motors specializes in selling cars to buyers...Ch. 19 - A process engineer is considering two sampling...Ch. 19 - Christina Sanders is a member of the womens...Ch. 19 - Erics Cookie House sells chocolate chip cookies in...Ch. 19 - The numbers of near misses recorded for the last...Ch. 19 - Prob. 35CECh. 19 - Swiss Watches, Ltd. purchases watch stems for...Ch. 19 - Automatic Screen Door Manufacturing Company...Ch. 19 - Prob. 38CE
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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
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