Question

A police department reports that the probabilities that a X burglaries will be reported in a given day are given below. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth A) B) 1.3 ơ 0.67 C) D) None of These P(X) 0 | 9.805e -6 1 0.0004430 20.008011 0.07239 40.3271 5| 0.5918 What is the standard deviation for this probability distribution?

Answer 1

Solution:

Mean of the probability distribution = summation(Xi*P(Xi))

=(0*0.000009805)+(1*0.0004430)+(2*0.008011)+(3*0.07239) +(4*0.3271)+(5*0.5018)

= 0+0.0004430+0.016022+0.21717+1.3084+2.959

= 4.50

Standard deviation can be calculated as

Sqrt(summation(Xi-mean)^2 *P(Xi)

Sqrt((0-4.5)^2×0.000256 +(1-4.5)^2×0.0004430 +(2-4.5)^2*0.008011 +(3-4.5)^2*0.07239+(4-4.5)^2*0.3271+(5-4.5)^2*0.5919

Sqrt(0.005184+0.00542675+0.05006875+0.164025+0.08175+0.147875)

=Sqrt(0.4543295)

= 0.6740

So its answer is B. I.e. 0.67