Question

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a
given day are 0.46, 0.41, 0.09, and 0.04, respectively. Find the standard deviation for the probability
distribution. Round answer to the nearest hundredth.
1.06
0.79
0.63
1.04

Answer 1

This problem involves binomial probability. Having forgotten the formula for the standard dev of such a distribution, I googled "standard deviation binomial distribution" and was presented with the following (among other hits):

http://www.statisticslectures.com/topics/meanstandarddeviationbinomial/

Please see what you can do with this information. Still have questions? Please ask.

Answer 2

This is just a discrete probability distribution, but not binomial, since we don't have a value of p = probability of success or any other information like number of trials. Instead, you would use the general formula for expected value for the average, E(X) = Sum (X*P(X)) and the standard deviation is
Standard Deviation for a Discrete Random Variable
σ=√(∑[(xi−μ)^2pi).
Use the expected value E(X) = ∑X*P(X) as the mean. For this data, E(X) = 0.71
To get the standard deviation:
Take each value of x (0, 1, 2, and 3) and subtract 0.71 from each. Square each of those numbers, and multiply by the probability.
((0-0.71)^2)(0.46) + ((1-0.71)^2)(0.41) + ((2-0.71)^2)(0.09) + ((3-0.71)^2)(0.04) = 0.6259
Then take the square root: sqrt(0.6259) = 0.79
Here is a link to the formula for E(X) and Std Dev(X), scroll down to the 2nd yellow box.

https://onlinecourses.science.psu.edu/stat200/node/36