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

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