Question

The unemployment rate of western states is 5.2%, for eastern states it is 5.6%, for southern states it is 4.9%, and for Midwestern states it is 5.8%. The western states comprise 13% of the labor force, the eastern states comprise 23% of the labor force, the southern states comprise 25% of the labor force, and the midwestern states comprise the remainder of the labor force. Find the unemployment rate for the nation. (please round your answer to 2 decimal places)

Answer 1

Ans:

UE=unemployed

Given that

P(UE/western)=0.052

P(UE/eastern)=0.056

P(UE/southern)=0.049

P(UE/midwestern)=0.058

P(western)=0.13

P(eastern)=0.23

P(southern)=0.25

P(midwestern)=1-0.13-0.23-0.25=0.39

So,

P(UE)

=P(UE/western)*P(western)+P(UE/eastern)*P(eastern)+P(UE/southern)*P(southern)+P(UE/midwestern)*P(midwestern)

=0.052*0.13+0.056*0.23+0.049*0.25+0.058*0.39

=0.0545 or 5.45%