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 (very dissatisfied) to a high of (very satisfied). Excel File: data05-21.xlsx Probability Job Satisfaction IS Senior IS Middle Score Executives Managers 1 0.05 0.04 2 0.09 0.10 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 (to 2 decimals)? b. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)? c. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals). Executives Middle managers d. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives Middle managers e. What comparison can you make about the job satisfaction of senior executives and middle managers? - Select your answer -

Answer 1

Kindly see explanation

Explanation:

Given the data:

JOB satisfaction (x) : 1, 2, 3, 4, 5

IS Senior ; p(x) : 0.05, 0.09, 0.03, 0.42, 0.41

IS Middle ; p(x) : 0.04, 0.10, 0.12, 0.46, 0.28

Expected value of job satisfaction for senior executives :

E(x) = Σp(x) * x = [(1*0.05) + (2*0.09) + (3*0.03) + (4*0.42) + (5*0.41)]

= 4.05

B) Σp(x) * x = [(1*0.04) + (2*0.10) + (3*0.12) + (4*0.46) + (5*0.28)]

= 3.84

C.) Job variance for executives:

Σ(x - E(x))² * p(x) :

((1 - 4.05)^2 * 0.05) + ((2 - 4.05)^2 * 0.09) + ((3 - 4.05)^2 * 0.03) + ((4 - 4.05)^2 * 0.42) + ((5 - 4.05)^2 * 0.41)

= 1.2475 = 1.25 ( using calculator)

job variance for middle managers :

Σ(x - E(x))² * p(x) :

((1 - 3.84)^2 * 0.04) + ((2 - 3.84)^2 * 0.10) + ((3 - 3.84)^2 * 0.12) + ((4 - 3.84)^2 * 0.46) + ((5 - 3.84)^2 * 0.28)

= 1.1344 = 1.13 (using calculator)

Standard deviation(sd) for (senior managers) :

sd = √variance

sd = √1.25 = 1.118 = 1.12

Standard deviation(sd) for (middle managers) :

sd = √variance

sd = √1.13 = 1.063 = 1.06

The expected value (mean) for senior executives (4.05) is slightly higher Than obtained for middle managers (3.84). Similarly the measure of Variation in job satisfaction ; standard deviation and variance is also higher for senior managers than in middle managers.