Answer to Question #114985 in Statistics and Probability for Emmanuel

Question

A recent study shows that the annual cost of maintaining a building in Texas averages
200 US Dollars with a variance of 260 US Dollars. 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 Texas.

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 Texas is $20.96.$