Question

let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of

X is as follows.

x	1	2	3	4	5
Px	0.66	0.11	0.08	0.02	0.13

Compute the standard deviation

σX. Round the answer to three decimal places.

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
1	0.66	0.66	0.66
2	0.11	0.22	0.44
3	0.08	0.24	0.72
4	0.02	0.08	0.32
5	0.13	0.65	3.25
Sum	1	1.85	5.39

Solution :

Mean = X * P(X)

= 1.85

Standard deviation =

=X 2 * P(X) - 2

=  5.39 - (1.85)2 = 1.9675

Standard deviation = = 1.403