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 0.06 0.04 2 0.09 0.10 3 0.03 0.13 4 0.42 0.45 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. executives middle managers (d) compute the standard deviation of job satisfaction scores for both probability distributions. (round your answers to two decimal places.) executives middle managers (e) compare the overall job satisfaction of senior executives and middle managers. the average score for senior executives is ---select--- the middle managers score. the standard deviation for senior executives is ---select--- the middle managers standard deviation.

Answer 1

The expected value of the job satisfaction score for senior executives is 3.98, and for middle managers it is 3.92. The variance of job satisfaction scores for senior executives is 1.1664, and for middle managers it is 1.0576. The standard deviation for senior executives is approximately 1.08, and for middle managers it is approximately 1.03. The average score for senior executives is slightly higher than for middle managers, and the standard deviation is also slightly higher for senior executives.

Step-by-step explanation:

(a) To find the expected value of the job satisfaction score for senior executives, we multiply each score by its corresponding probability and sum the results. It can be calculated as follows:

Expected Value = (1 * 0.06) + (2 * 0.09) + (3 * 0.03) + (4 * 0.42) + (5 * 0.40) = 3.98

(b) To find the expected value of the job satisfaction score for middle managers, we use the same method:

Expected Value = (1 * 0.04) + (2 * 0.10) + (3 * 0.13) + (4 * 0.45) + (5 * 0.28) = 3.92

(c) To compute the variance for senior executives, we subtract the expected value from each score, square the result, multiply it by the corresponding probability, and sum the results:

Variance = [(1-3.98)^2 * 0.06] + [(2-3.98)^2 * 0.09] + [(3-3.98)^2 * 0.03] + [(4-3.98)^2 * 0.42] + [(5-3.98)^2 * 0.40] = 1.1664

Similarly, the variance for middle managers can be calculated:

Variance = [(1-3.92)^2 * 0.04] + [(2-3.92)^2 * 0.10] + [(3-3.92)^2 * 0.13] + [(4-3.92)^2 * 0.45] + [(5-3.92)^2 * 0.28] = 1.0576

(d) To find the standard deviation for both distributions, we take the square root of their respective variances:

Standard Deviation for Senior Executives = √1.1664 ≈ 1.08

Standard Deviation for Middle Managers = √1.0576 ≈ 1.03

(e) To compare overall job satisfaction, we can compare the average score (expected value) and the standard deviation. The average score for senior executives is higher (3.98) compared to middle managers (3.92). However, the standard deviation for senior executives is slightly higher (1.08) compared to middle managers (1.03).