Question

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution.

x f(x)
0 0.80
1 0.15
2 0.04
3 0.01

The mean and the standard deviation for the number of electrical outages (respectively) are:

a. 2.6 and 5.77
b. 0.26 and 0.577
c. 3 and 0.01
d. 0 and 0.8

Answer 1

b) mean = 0.26, standard deviation = 0.577

Explanation:

mean is given be formula:

`\mu=\sum xf(x)\\\mu= (0)(.8)+(1)(.15)+(2)(0.04)+(3)(0.01)\\\mu=0.26`

Standard deviation:

`\sigma=\sqrt{\sum (x-\mu)^(2)f(x)} \\=\sqrt{(0-0.26)^(2)(0.80)+(1-0.26)^(2)(0.15)+(2-0.26)^(2)(0.04)+(3-0.26)^(2)(0.01)} \\=√(0.054+0.0812+.1211+0.075) \\=0.577`