Question

Choose an American household at random and let the random variable X be the number of vehicles they own. Here is the probability distribution if we ignore the few households that own more than 5 vehicles:

X	0	1	2	3	4	5
P(X=x)	0.09	0.36	0.35	0.13	0.05	0.02

a) What is the probability a household picked at random will own more than 3 vehicles?

b) What is the mean and standard deviation?

Answer 1

Solution

x	P(x)	x * P(x)	x2 * P(x)
0	0.09	0	0
1	0.36	0.36	0.36
2	0.35	0.7	1.4
3	0.13	0.39	1.17
4	0.05	0.2	0.8
5	0.02	0.1	0.5
	1	1.75	4.23

a ) P ( X > 3 ) =   P ( x = 4 ) + P ( x = 5 )

= 0.05 +0.02

= 0.07

P ( X > 3 ) = 0.07

b ) Mean = = X * P(X) = 1.75

Standard deviation = =X 2 * P(X) - 2  

   =4.23 -3.0625

=1.1675

= 1.0805

Standard deviation =1.08