Question

The percent frequency distributions of job satisfaction scores for a sample of information systems (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	27	13
4	42	46
5	17	27

If required, round your answers to two decimal places.

(a)	Develop a probability distribution for the job satisfaction score of a randomly selected senior executive.
	x f(x) 1 2 3 4 5
(b)	Develop a probability distribution for the job satisfaction score of a randomly selected middle manager.
	x f(x) 1 2 3 4 5
(c)	What is the probability that a randomly selected senior executive will report a job satisfaction score of 4 or 5?
(d)	What is the probability that a randomly selected middle manager is very satisfied?
(e)	Compare the overall job satisfaction of senior executives and middle managers.
	Senior executives appear to be more satisfied/less satisfied than middle managers.

Answer 1

The percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers are as follows

Job Satisfaction Score	IS Senior Executives (%)	IS Middle Managers (%)
1	5	4
2	9	10
3	27	13
4	42	46
5	17	27

Total 100 100   

a) A probability distribution for the job satisfaction score of a randomly selected senior executive is given by

x	f(x)
1	5/100=0.05
2	9/100=0.09
3	27/100=0.27
4	42/100=0.42
5 17/100=0.17

b) A  probability distribution for the job satisfaction score of a randomly selected middle manager is given by:

x	f(x)
1	4/100=0.04
2	10/100=0.10
3	13/100=0.13
4	46/100=0.46
5	27/100=0.27

c) the probability that a randomly selected senior executive will report a job satisfaction score of 4 or 5 is = P(X=4)+P(X=5)

=0.42+0.17

=0.59

d) the probability that a randomly selected middle manager is very satisfied=P(X=5)

=0.27

e) The expected job satisfaction for the senior executive is given by:

The expected job satisfaction for the middle executive is given by:

Comparing the expected job satisfactions for two types of executives the Senior executives appear to be more satisfied satisfied than middle managers.