Question

A store sells bags of dog food. Let X be the number of bags sold to the next customer. The probability distribution for X is given below. Find the variance for the number of bags sold. Give your answer to four decimal places and do not give units.

x	1	2	3	4	5
P(X=x)	0.52	0.37	0.06	0.04	0.01

Answer 1

X	P(X=x)	X2	X * P(X=x)	X2 * P(X=x)
1	0.52	1	0.52	0.52
2	0.37	4	0.74	1.48
3	0.06	9	0.18	0.54
4	0.04	16	0.16	0.64
5	0.01	25	0.05	0.25
Total	1	55	1.65	3.43

Mean  

μ = ΣΧ* P(x)) = 1.65

Variance

σ' = Σ(X2 * P(X) – (μ):

o2 = 3.43 - (1.65)

02 = 0.7075