# Standard Deviation Problem

• Apr 18th 2010, 12:55 PM
hasanbalkan
Standard Deviation Problem
I would appreciate your help on the following problem:

A mason is contracted to build a patio retaining wall. Plans call for the base of the wall to be a row of 50 10-inch bricks, each separated by $\displaystyle \frac{1}{2}$-inch-thick mortar. Suppose that the bricks used are randomly chosen from a population of bricks whose mean length is 10 inches and whose standard deviation is $\displaystyle \frac{1}{32}$ inch. Also, suppose that the mason, on the average, will make the mortar $\displaystyle \frac{1}{2}$ inch thick, but the actual dimension varies from brick to brick, the standard deviation of the thickness being $\displaystyle \frac{1}{16}$ inch. What is the standard deviation of the length of the first row of the wall?

• Apr 18th 2010, 10:22 PM
CaptainBlack
Quote:

Originally Posted by hasanbalkan
I would appreciate your help on the following problem:

A mason is contracted to build a patio retaining wall. Plans call for the base of the wall to be a row of 50 10-inch bricks, each separated by $\displaystyle \frac{1}{2}$-inch-thick mortar. Suppose that the bricks used are randomly chosen from a population of bricks whose mean length is 10 inches and whose standard deviation is $\displaystyle \frac{1}{32}$ inch. Also, suppose that the mason, on the average, will make the mortar $\displaystyle \frac{1}{2}$ inch thick, but the actual dimension varies from brick to brick, the standard deviation of the thickness being $\displaystyle \frac{1}{16}$ inch. What is the standard deviation of the length of the first row of the wall?

$\displaystyle L=(X_1+ ... + X_{50}) + (Y_1+ ... + Y_{49})$
Where the $\displaystyle X$'s are RVs corresponding to the length of the 50 bricks and the $\displaystyle Y$'s are RVs corresponding to the thickness of the mortar between consecutive bricks, and these are all independedntly distributed.