Question

Complete parts​ (a) and​ (b) below. The number of dogs per household in a small town

Dogs 0 1 2 3 4 5

Probability 0.649 0.220 0.087 0.024 0.013 0.008 ​

(a) Find the​ mean, variance, and standard deviation of the probability distribution.

Answer 1

Solution

x	P(x)	x * P(x)	x2 * P(x)
0	0.649	0	0
1	0.22	0.22	0.22
2	0.087	0.174	0.348
3	0.024	0.072	0.216
4	0.013	0.052	0.208
5	0.008	0.04	0.2
	1.001	0.558	1.192

a) Mean = = X * P(X) = 0.558

b ) Variance = ² =X ² * P(X) - ²  

  =1.192 - 0.31136

    = 0.881

Variance = 0.881

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

=1.192 - 0.31136

=0.881

= 0.938

Standard deviation = 0.938