Answer:
0.748
Step-by-step explanation:
We have to find the standard deviation of the number of homes sold=S.D(x)
[tex]S.D(x)=\sqrt{sum[x^{2}*p(x)]-[sum(x*p(x))]^2 }[/tex]
Number sold x   Probability p(x)  x*p(x)    x²    x²*p(x)
0 Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.2 Â Â Â Â Â Â Â Â Â Â Â 0 Â Â Â Â Â 0 Â Â Â Â Â 0
1 Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4 Â Â Â Â Â Â Â Â Â Â Â 0.4 Â Â Â Â 1 Â Â Â Â Â Â 0.4
2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.4 Â Â Â Â Â Â Â Â Â Â Â 0.8 Â Â Â Â 4 Â Â Â Â Â 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.
