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Let's break down and solve each part of this problem step-by-step.

### Part (a): Average Score of Job Satisfaction
The average score, also known as the **expected value (E[X])**, is calculated using the formula:
\[
E[X] = \sum (x \cdot P(x))
\]
where $ x $ is each job satisfaction score and $ P(x) $ is the corresponding probability (proportion of score).

Given values:
- For score 1: $ P(1) = 0.11 $
- For score 2: $ P(2) = 0.17 $
- For score 3: $ P(3) = 0.29 $
- For score 4: $ P(4) = 0.43 $

Now, calculate $ E[X] $:
\[
E[X] = (1 \cdot 0.11) + (2 \cdot 0.17) + (3 \cdot 0.29) + (4 \cdot 0.43)
\]
\[
E[X] = 0.11 + 0.34 + 0.87 + 1.72 = 3.04
\]
So, the **average score** is **3.04** points.

### Part (b): Standard Deviation of Job Satisfaction
The **standard deviation** is calculated as the square root of the variance, where:
\[
\text{Variance} = E[X^2] - (E[X])^2
\]
1. First, calculate $ E[X^2] $:
   \[
   E[X^2] = \sum (x^2 \cdot P(x))
   \]
   \[
   E[X^2] = (1^2 \cdot 0.11) + (2^2 \cdot 0.17) + (3^2 \cdot 0.29) + (4^2 \cdot 0.43)
   \]
   \[
   E[X^2] = (1 \cdot 0.11) + (4 \cdot 0.17) + (9 \cdot 0.29) + (16 \cdot 0.43)
   \]
   \[
   E[X^2] = 0.11 + 0.68 + 2.61 + 6.88 = 10.28
   \]

2. Now, calculate the variance:
   \[
   \text{Variance} = E[X^2] - (E[X])^2
   \]
   \[
   \text{Variance} = 10.28 - (3.04)^2
   \]
   \[
   \text{Variance} = 10.28 - 9.2416 = 1.0384
   \]

3. Finally, the standard deviation is the square root of the variance:
   \[
   \text{Standard Deviation} = \sqrt{1.0384} \approx 1.018
   \]
So, the **standard deviation** is approximately **1.018** points.

### Part (c): Expected Yearly Promotion Raise
To calculate the expected yearly promotion raise, use the formula:
\[
\text{Expected Raise} = (E[X] \cdot \text{raise per score point}) + \text{fixed raise} + \text{cost of living adjustment}
\]
Given:
- Raise per score point = $4200
- Fixed raise = $150
- Cost of living adjustment = $350

Using $ E[X] = 3.04 $:
\[
\text{Expected Raise} = (3.04 \cdot 4200) + 150 + 350
\]
\[
\text{Expected Raise} = 12768 + 150 + 350 = 13268
\]
So, the **expected yearly promotion raise** is **$13,268**.

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Let me know if you'd like further details or have questions!

### Additional Related Questions:
1. What is the probability of getting a job satisfaction score of 4?
2. How would the average score change if the probability of a score of 4 increased?
3. What is the effect of the standard deviation on the spread of satisfaction scores?
4. How does adding a fixed raise and cost of living adjustment impact the expected promotion raise?
5. How would the standard deviation change if scores were distributed more evenly?

### Tip:
When calculating expected values, ensure that the probabilities sum to 1 for accurate results.

The following probability distribution of job satisfaction scores for a sample of information system(IS) senior executives range from a low of 1 (very dissatisfied) to a high of 4 (very satisfied) is given below:

(a) What is the average score of the job satisfaction for senior executives?
(b) What is the standard deviation of the job satisfaction for senior executives?
(c) If a senior executive expects to earn an additional $4200 per year for each job satisfaction score point, and there was a $150 yearly fixed raise and an extra $350 for cost of living adjustment, what is the expected yearly promotion raise for this senior executive?

Learn how to calculate the average job satisfaction score, standard deviation, and expected yearly promotion raise for senior executives based on a probability distribution of satisfaction scores. This detailed solution covers expected value, variance, and real-life application for financial adjustments.

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