1. ## 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 $\frac{1}{2}$-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 $\frac{1}{32}$ inch. Also, suppose that the mason, on the average, will make the mortar $\frac{1}{2}$ inch thick, but the actual dimension varies from brick to brick, the standard deviation of the thickness being $\frac{1}{16}$ inch. What is the standard deviation of the length of the first row of the wall?

2. 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 $\frac{1}{2}$-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 $\frac{1}{32}$ inch. Also, suppose that the mason, on the average, will make the mortar $\frac{1}{2}$ inch thick, but the actual dimension varies from brick to brick, the standard deviation of the thickness being $\frac{1}{16}$ inch. What is the standard deviation of the length of the first row of the wall?

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