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?

0.748

Step-by-step explanation:

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

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.