Question

The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).

Job Satisfaction Score	Probability
	IS Senior Executives	IS Middle Managers
1	0.05	0.04
2	0.09	0.10
3	0.04	0.12
4	0.42	0.46
5	0.40	0.28

(a)

What is the expected value of the job satisfaction score for senior executives?

(b)

What is the expected value of the job satisfaction score for middle managers?

(c)

Compute the variance of job satisfaction scores for executives and middle managers.

executivesmiddle managers

(d)

Compute the standard deviation of job satisfaction scores for both probability distributions. (Round your answers to two decimal places.)

executivesmiddle managers

(e)

Compare the overall job satisfaction of senior executives and middle managers.

The average score for senior executives is (lower than? higher than? equal to?) the middle managers score. The standard deviation for senior executives is (lower than, higher than, equal to) the middle managers standard deviation.

Answer 1

For probability distribution of the job satisfaction score for senior executives:

Let X is a random variable shows the job satisfaction score for senior executives. Following table shows the calculations:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
1	0.05	0.05	0.05
2	0.09	0.18	0.36
3	0.04	0.12	0.36
4	0.42	1.68	6.72
5	0.4	2	10
Total	1	4.03	17.49

The expected value is

The variance is

The standard deviation is

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For probability distribution of the job satisfaction score for middle Managers:

Let Y is a random variable shows the job satisfaction score for middle managers. Following table shows the calculations:

Y	P(Y=y)	yP(Y=y)	y^2*P(Y=y)
1	0.04	0.04	0.04
2	0.1	0.2	0.4
3	0.12	0.36	1.08
4	0.46	1.84	7.36
5	0.28	1.4	7
Total	1	3.84	15.88

The expected value is:

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(a) 4.03

(b) 3.84

(c)

senor executive: 1.2491

middle managers 1.1344

(d)

senor executive: 1.12

middle managers 1.07

(e)

The average score for senior executives is higher than the middle managers score. The standard deviation for senior executives is higher than the middle managers standard deviation.