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

Answer:

Mean = 2.14

Standard deviation = 2.40

Step-by-step explanation:

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

$X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52$

= 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

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

After solving the above equation we will get

= 5.78

Now, the standard deviation is $= \sqrt{Variance}$

$= \sqrt{5.78}$

= 2.404163056

or

= 2.40