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 standard deviation of the annual cost of maintaining a building in Accra.

Answer 1

$\text {Let Y represents the annual cost of maintaining}\\ \text { a building in Accra, then, E(Y)=200, V(Y)=260,}\\ \text {Let X represents the annual cost of maintaining}\\ \text { a building in Accra after adding a tax of 30\%,}\\ X=1.3Y\\ V(X)=V(1.30Y)=1.30^{2}V(Y)\\ =1.30^{2}(260)=439.4,\\ \therefore \sigma_{X}=\sqrt{V(X)}=\sqrt{439.4}=20.962$