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 SatisfactionScore IS Senior Executives Probability IS Middle Managers
1 0.05 0.04
2 0.09 0.1
3 0.03 0.12
4 0.42 0.46
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.
d. Compute the standard deviation of job satisfaction scores for both probability distributions.
e. Compare the overall job satisfaction of senior executives and middle managers.

Answer 1

Answer:

a. 4.05 b. 3.84 c. 1.2475 and 1.1344 d. 1.1169 and 1.0651  e. We can say that the overall job satistaction of senior executives and middle managers is about 4; however, there is more variability in the job satisfaction for senior executives than in the job satisfaction for middle managers.

Step-by-step explanation:

a. (1)(0.05)+(2)(0.09)+(3)(0.03)+(4)(0.42)+(5)(0.41) = 4.05

b. (1)(0.04)+(2)(0.1)+(3)(0.12)+(4)(0.46)+(5)(0.28) = 3.84

c. We compute the variances as follow: $[(1)^2(0.05)+(2)^2(0.09)+(3)^2(0.03)+(4)^2(0.42)+(5)^2(0.41)] - 4.05^2$ = 1.2475 and $[(1)^2(0.04)+(2)^2(0.1)+(3)^2(0.12)+(4)^2(0.46)+(5)^2(0.28)]-3.84^2$ = 1.1344

d. The standard deviation is the squared root of the variance, therefore, we have $\sqrt{1.2475} = 1.1169$ and $\sqrt{1.1344} = 1.0651$

e. The expected value of the job satisfaction score for senior executives is very similar to the job satisfaction score for middle managers. We can say that the overall job satistaction of senior executives and middle managers is about 4; however, there is more variability in the job satisfaction for senior executives than in the job satisfaction for middle managers.