Respuesta :
Answer:
1.)E₁ = 4,03
2) E₂ = 3,85
3) σ₁² = 1,23
4)σ₂² = 1,14
5)σ₁ = 1,11
6)σ₂ = 1,07
5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median 0,18 and difference in standard deviation 0,04
Step-by-step explanation:
1.-Expected value of the job satisfaction score for senior executive
E₁, variance σ₁ and standard deviation σ₁ and expected value of the job satisfaction score for Middle Manager E₂ variance σ₂ and standard deviation σ₂
E(X) = ∑ ( xi *f(xi)
JSS IS senior executive IS Middle Managers
1 0,05 0,04
2 0,09 0,1
3 0,03 0,12
4 0,44 0,45
5 0,39 0,29
∑ xi*f(xi) = 1*0,05 + 2 *0,09 + 3*0,03 + 4 * 0,44 + 5 * 0,39
E₁ = 0,05 + 0,18 + 0,09 + 1,76 + 1,95
1.)E₁ = 4,03
2.) ∑ xi*f(xi)
E₂ = 1* 0,04 + 2 * 0,1 + 3*0,12 + 4*0,45 +5*0,29
E₂ = 0,04 + 0,2 + 0,36 + 1,8 + 1,45
E₂ = 3,85
2 ) E₂ = 3,85
3) Variance of job satisfaction scores for senior executives.
x² f(x) x²* f(x)
1 0,05 0,05
4 0,09 0,36
9 0,03 0,27
16 0,44 7,04
25 0,39 9,75
σ₁² = [ ∑ x²*f(x) ] - μ² ∑ x²*f(x) = 17,47
In this case μ = E μ² = ( 4,03)² = 16,24
For senior executives: σ₁² = 17,47 - 16,24 = 1,23
σ₁² = 1,23
And standard deviation σ₁ = 1,11
For Middle managers
x² f(x) x²* f(x)
1 0,04 0,04
4 0,1 0,4
9 0,12 1,08
16 0,45 7,2
25 0,29 7,25
∑ x²*f(x) = 15,97
σ₂² = 15,97 - (3,85)² = 15,97 - 14,82
σ₂² = 1,14
σ₂ = √1,14 = 1,07
5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median 0,18 and difference in standard deviation 0,04
