1. For unemployed persons in the United States, the average number of months of
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Question
1. For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months. Suppose the following data are for particular region in upstate New York. The values in the first columns 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 b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution c. What is the probability that a person is unemployed for two months or less? Unemployed for months than two months? d. What is the probability that a person is unemployed for more than six months? 2. The percent frequency distributions of jobs satisfaction sores for a sample of information system (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied) Job satisfaction Score IS Senior Executives (%) IS Middle Managers (%) 1 5 4 2 9 10 3 3 12 4 42 46 5 41 28 a. Develop a probability distribution for the job satisfaction score of a senior executive b.Develop a probability distribution for the job satisfaction score of a senior manager c. What is the probability a senior executive will report a job satisfaction score of 4 or 5? d.What is the probability a middle manager is very satisfied? e. Compare the overall job satisfaction of senior executives and middle managers 1. For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months. Suppose the following data are for particular region in upstate New York. The values in the first columns 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 b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution c. What is the probability that a person is unemployed for two months or less? Unemployed for months than two months? d. What is the probability that a person is unemployed for more than six months? 2. The percent frequency distributions of jobs satisfaction sores for a sample of information system (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied) Job satisfaction Score IS Senior Executives (%) IS Middle Managers (%) 1 5 4 2 9 10 3 3 12 4 42 46 5 41 28 a. Develop a probability distribution for the job satisfaction score of a senior executive b.Develop a probability distribution for the job satisfaction score of a senior manager c. What is the probability a senior executive will report a job satisfaction score of 4 or 5? d.What is the probability a middle manager is very satisfied? e. Compare the overall job satisfaction of senior executives and middle managersExplanation / Answer
Answer:
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months. Suppose the following data are for particular region in upstate New York. The values in the first columns show the corresponding number of unemployed persons
Let x be a random variable indicating the number of months a person is unemployed.
Months Unemployed
Number Unemployed
Probability P
1
1029
0.0381
2
1686
0.0625
3
2269
0.0841
4
2675
0.0992
5
3487
0.1293
6
4652
0.1725
7
4145
0.1537
8
3587
0.1330
9
2325
0.0862
10
1120
0.0415
Total
26975
1.0
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution
All probabilities are between 0 and 1, sum of the probabilities is 1. The conditions for a valid discrete probability distribution are satisfied.
c. What is the probability that a person is unemployed for two months or less?
P =0.0381+0.0625 =0.1006
Unemployed for months than two months?
P= 1-0.1006 =0.8994
d. What is the probability that a person is unemployed for more than six months?
P=0.1537+0.1330+0.0862+0.0415 = 0.4144
2. The percent frequency distributions of jobs satisfaction sores for a sample of information system (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very dissatisfied).
Job satisfaction Score
IS Senior Executives (%)
Probability
1
5
0.05
2
9
0.09
3
3
0.03
4
42
0.42
5
41
0.41
Total
100
1.0
b.Develop a probability distribution for the job satisfaction score of a senior manager
Job satisfaction Score
IS Middle Managers (%)
Probability
1
4
0.04
2
10
0.1
3
12
0.12
4
46
0.46
5
28
0.28
Total
100
1.0
What is the probability a senior executive will report a job satisfaction score of 4 or 5?
P=0.42+0.41=0.83
d.What is the probability a middle manager is very satisfied? P=0.28
e. Compare the overall job satisfaction of senior executives and middle managers
On the overall job satisfaction of senior executives and middle managers are mostly satisfied or very satisfied.
Months Unemployed
Number Unemployed
Probability P
1
1029
0.0381
2
1686
0.0625
3
2269
0.0841
4
2675
0.0992
5
3487
0.1293
6
4652
0.1725
7
4145
0.1537
8
3587
0.1330
9
2325
0.0862
10
1120
0.0415
Total
26975
1.0
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