Question

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.41, 0.05, and 0.04, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth.

Answer 1

Your data:

X P(X)

0 0.50
1 0.41
2 0.05
3 0.04

Here's a formula for the mean:
SUM[X * P(X)]
(Take each X times its respective P(X), then sum for a total. This will be your mean.)

Here's a formula for the standard deviation:
SQRT of {SUM[X^2 * P(X)] - mean^2}
(Square each X. Take each X^2 times its respective P(X), then sum for a total. Subtract mean^2 from this value. Then take the square root of that result. This will be your standard deviation.)

I hope this will help get you started.

Answer 2

0.57