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

$\text {Let Y represents the annual cost of maintaining}\\ \text { a building in Accra, then, E(Y)=200, V(Y)=260,}\\ \text {Let K represents the annual cost of maintaining}\\ \text { a building in Accra after adding a tax of 30\%,}\\ K=1.3Y\\ V(K)=V(1.3Y)=1.3^{2}V(Y)\\ =1.30^{2}(260)=439.4,\\ \therefore \sigma_{K}=\sqrt{V(K)}=\sqrt{439.4}=20.96$