Answer:
[tex]\sigma_x = 0.57[/tex]
Step-by-step explanation:
Given
[tex]\mu_x = 6[/tex]
See attachment
Required
Calculate [tex]\sigma_x[/tex]
This is calculated as:
[tex]\sigma_x = \sqrt{Var(x)}[/tex]
Where
[tex]Var(x) =\sum (x - \mu_x)^2 * P(x)[/tex]
So, we have:
[tex]Var(x) =(0 - 0.4)^2 * 0.64 + (1 - 0.4)^2 * 0.32 + (2 - 0.4)^2 * 0.04[/tex]
Using a calculator
[tex]Var(x) =0.32[/tex]
[tex]\sigma_x = \sqrt{Var(x)[/tex]
[tex]\sigma_x = \sqrt{0.32[/tex]
[tex]\sigma_x = 0.57[/tex] --- approximated
