The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution 
. If X is the molarity of a solution of sodium chloride (NaCl), and Y is the molarity of a solution of sodium carbonate
, the molarity of sodium ion (Na+) in a solution made of equal parts NaCl and is given by M = 0.5X + Y. Assume X and Y are independent and normally distributed, and that X has mean 0.450 and standard deviation 0.050, and Y has mean 0.250 and standard deviation 0.025.
a. What is the distribution of M?
b. Find P(M > 0.5).
(a) Since M is a linear combination of independent normal random variables, M is normally distributed.
(b)
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