Question

The following probability model represents the number of children living in apartments at a large complex.

x 0 1 2 3 4

P(X=x) 0.11 0.22 0.45 0.19 0.03

Use the probability model to find the following: Find the expected number of children living in an apartment at this complex. Find the standard deviation for the number of children living in an apartment at this complex.

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
0	0.11	0	0
1	0.22	0.22	0.22
2	0.45	0.9	1.8
3	0.19	0.57	1.71
4	0.03	0.12	0.48
Sum	1	1.81	4.21

Mean = X * P(X)

= 1.81

Standard deviation =

=X ² * P(X) - ²

=  4.21 - (1.81)² = 0.9339

Standard deviation = = 0.9664