Answer:
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.
