Answer to Question #116227 in Statistics and Probability for felix

Question

A7. 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

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