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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 sodium chloride (NaCl), and Y is the molarity of a solution of sodium carbonate (Na_{2}CO_{3}), the molarity of sodium ion (Na^{+}) in a solution made of equal parts NaCl and Na_{2}CO_{3} 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).

The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

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