Question

Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13

Answer 1

Mean = 2.14

Standard deviation = 2.40

Explanation:

The calculation of mean and standard deviation is shown below:-

`X = .07*0 + 0.20* 1 + 0.38* 2 + 0.22* 3 + 0.13* 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52`

= 2.14

So, the mean is 2.14

Now, For computing the standard deviation first we need to find out the variance which is shown below:-

Variance is

`Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07* (0^2) + .20* (0^1) + .38* (0^2) + .22* (0^3) +0.13* (0^4)`

After solving the above equation we will get

= 5.78

Now, the standard deviation is
`= √(Variance)`

`= √(5.78)`

= 2.404163056

or

= 2.40