x 0 1 2 3 4 5
P(x) 0.206 0.360 0.226 0.162 0.035 0.001
a)probability that one or more of the five parolees will be
repeat offenders=1-probability that less than one of the five
parolees will be repeat offender =1-probability that less than one
of the five parolees will be repeat offender =
=1-0.206 =0.794
b)probability that two or more of the five parolees will be
repeat offenders=1-robability that one or less than one of the five
parolees will be repeat offenders=1-P(0)-P(1)
=1-(0.206+0.360)=0.434
c)probability that four or more of the five parolees will be
repeat offenders=P(4)+P(5)=0.035+0.001=0.036
d)expected no
offfenders=0*(0.206)+1*(0.360)+2(0.226)+3*(0.162)+4*(0.035)+5*(0.001)=1.443
e)variance=(0-1.443)^2*(0.206)+(1-1.443)^2*(0.360)+(2-1.443)^2*(0.226)+(3-1.443)^2*(0.162)+(4-1.443)^2*(0.035)+(5-1.443)^2*(0.001)
=0.4289 + 0.0706 +0.0701+0.4142 +0.2288+0.0035 =1.22
standard deviation=sqrt(1.22)=1.10
