Answer:
Step-by-step explanation:
To calculate ;
1) the expected value of the job satisfaction score for senior executives ;
expected value = Summation (Px)
= 1 x 0.05 + 2 x 0.09 + 3 x 0.03 + 4 x 0.42 + 5 x 0.41
= 4.05
2) the expected value of the job satisfaction score for middle managers;
= 1 x 0.04 + 2 x 0.10 + 3 x 0.12 + 4 x 0.46 + 5 x 0.28
= 3.84
c) the variance of job satisfaction scores for executives and middle managers (to 2 decimals).
Executives ; Variance = Summation(PX^2 - Summation(PX)^2
i) For Executive Managers = 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2 = 1.246 = 1.25
ii) for middle managers ; 1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 = 1.134 = 1.13
d) the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives, Middle managers;
For Executives = square root [ 1 x 0.05 + 2^2 x 0.09 + 3^2 x 0.03 + 4^2 x 0.42 + 5^2 x 0.41 - 4.05^2] = 1.12
For Middle Managers ; Square root [1 x 0.04 + 2^2 x 0.10 + 3^2 x 0.12 + 4^2 x 0.46 + 5^2 x 0.28 - 3.84^2 ] = 1.06
e) from the values gotten for the variance of both executive and middle managers, the variance of the former is more than that of the latter as such higher satisfaction with the executive managers.
, to find that 
. Plugging 
ordered pairs into g(x), we see that a = 1. For example, for 
, 
. Solving for a gives 1.