Answer to Question #119390 in Statistics and Probability for Michael

Question

A recent study shows that the annual cost of maintaining a building in Accra averages
200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items
associated with the maintenance of building i.e. everything is made 30% more expensive.
Calculate the variance of the annual cost of maintaining a building in Accra.

Answer 1

Let X represents the annual cost of maintaining a building in Accra, then, E(x)=200, V(x)=260,Let Y represents the annual cost of maintaining a building in Accra after adding a tax of 30%,Y=1.3X

V(Y)=V(1.3X)=1.3²V(x)=1.3²(260)=439.4