Answer to Question #115404 in Statistics and Probability for Popcy

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

$$V(X)=\sigma^2=\sum(x_i-\mu)^2p(x_i)$$

$$V(aX)=\sigma_{aX}^2=a^2 V(X)$$

$$V(1.3X)=1.3^2V(X)=1.69(260)=439.4$$

$$\sigma_{1.3X}=\sqrt{V(1.3X)}=\sqrt{439.4}\approx20.96$$

The standard deviation of the annual cost of maintaining a building in Accra is $20.96.$