The following probability distributions of jobsatisfaction scores for a sample of informationsystems (is) senior executives and is middle managersrange from a low of 1 (very dissatisfied) to a high of5 (very satisfied).probability job satisfaction score is seniorexecutives 1 .05 2 .093 .03 4 .425 .41is middle managers.04.10.12.46.28a. what is the expected value of the job satisfactionscore for senior executives? b. what is the expected value of the job satisfactionscore for middle managers? c. compute the variance of job satisfaction scores forexecutives and middle managers. d. compute the standard deviation of job satisfactionscores for both probability distributions. e. compare the overall job satisfaction of seniorexecutives and middle managers.

a) 4.076

b) 3.9

c) variance for executives=1.128

variance for middle mangers=0.73

d)standard deviation for executives=1.062

standard deviation for middle mangers=0.854

e) Overall job satisfaction for senior executives is higher than middle manager.

Step-by-step explanation:

IS senior executives

Job Satisfaction       1    2          3       4     5

Probability          0.05 0.093 0.03 0.425 0.41

IS middle manager

Job Satisfaction  1       2    3        4    5

Probability         0.01 0.1 0.12 0.46 0.28

Let X denotes IS senior executive and Y denotes IS middle manager.

a)

E(X)=∑x*p(x)=1*0.05+2*0.093+3*0.03+4*0.425+5*0.41

E(X)=0.05+0.186+0.09+1.7+2.05

E(X)=4.076

b)

E(Y)=∑y*p(y)=1*0.1+2*0.1+3*0.12+4*0.46+5*0.28

E(Y)=0.1+0.2+0.36+1.84+1.4

E(Y)=3.9

c)

V(x)=∑x²*p(x)-(∑x*p(x))²

∑x²*p(x)=1*0.05+4*0.093+9*0.03+16*0.425+25*0.41

∑x²*p(x)=0.05+0.372+0.27+6.8+10.25

∑x²*p(x)=17.742

V(x)=17.742-(4.076)²

V(x)=1.128

V(y)=∑y²*p(y)-(∑y*p(y))²

∑y²*p(y)=1*0.1+4*0.1+9*0.12+16*0.46+25*0.28

∑y²*p(y)=0.1+0.4+1.08+7.36+7

∑y²*p(y)=15.94

V(y)=15.94-(3.9)²

V(y)=0.73

d)

S.D(x)=√V(x)

S.D(x)=√1.128

S.D(x)=1.062

S.D(y)=√V(y)

S.D(y)=0.854

e)

Overall job satisfaction for senior executives is more than middle manager as expected value of senior executives is greater than expected value of middle manger with relatively higher variability than middle manager.