Question

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold Probability 0 0.20 1 0.40 2 0.40 What is the standard deviation of the number of homes sold by the realtor during a month?

Answer 1

0.748

Explanation:

We have to find the standard deviation of the number of homes sold=S.D(x)

`S.D(x)=\sqrt{sum[x^(2)*p(x)]-[sum(x*p(x))]^2 }`

Number sold x Probability p(x) x*p(x) x² x²*p(x)

0 0.2 0 0 0

1 0.4 0.4 1 0.4

2 0.4 0.8 4 1.6

sum[x²*p(x)]=0+0.4+1.6=2

sum(x*p(x))=0+0.4+0.8=1.2

S.D(x)=√2-(1.2)²

S.D(x)=√2-1.44

S.D(x)=√0.56

S.D(x)=0.748.

Thus, the standard deviation of the number of homes sold by the realtor during a month is 0.748.