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	0.03	0.13
4	0.42	0.45
5	0.41	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  ---Select--- lower than higher than equal to the middle managers score. The standard deviation for senior executives is  ---Select--- lower than higher than equal to the middle managers standard deviation.

Answer 1

for senior executives:

x	f(x)	xP(x)	x2P(x)
1	0.0500	0.0500	0.0500
2	0.0900	0.1800	0.3600
3	0.0300	0.0900	0.2700
4	0.4200	1.6800	6.7200
5	0.4100	2.0500	10.2500
	total	4.0500	17.6500
	E(x) =μ=	ΣxP(x) =	4.0500
	E(x2) =	Σx2P(x) =	17.6500
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.2475
	std deviation=	σ= √σ2 =	1.1169

for   middle managers

x	f(x)	xP(x)	x2P(x)
1	0.0400	0.0400	0.0400
2	0.1000	0.2000	0.4000
3	0.1300	0.3900	1.1700
4	0.4500	1.8000	7.2000
5	0.2800	1.4000	7.0000
	total	3.8300	15.8100
	E(x) =μ=	ΣxP(x) =	3.8300
	E(x2) =	Σx2P(x) =	15.8100
	Var(x)=σ2 =	E(x2)-(E(x))2=	1.1411
	std deviation=	σ= √σ2 =	1.0682

a)

  expected value of the job satisfaction score for senior executives =4.05

b)

expected value of the job satisfaction score for middle managers =3.83

c)

variance of job satisfaction scores for executives =1.2475

variance of job satisfaction scores for middle managers =1.1411

d)

standard deviation of job satisfaction scores for  senior executives =1.1169

standard deviation of job satisfaction scores for  middle managers =1.0682

e)

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