1.  The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 10 23 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2 ), and Y is the molarity of a solution of ferric chloride (FeCl3 ), the molarity of chloride ion (Cl− ) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10.

a.   Find μM.

b.   Assuming X and Y to be independent,find σM.

2.  A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine.

a.  Find the mean of the total volume of the beverage in the case.

b.  Find the standard deviation of the total volume of the beverage in the case.

c.   Find the mean of the average volume per bottle of the beverage in the case.

d.  Find the standard deviation of the volume per bottle of the beverage in the case.

e.  How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?