On three examinations, you have grades of 88, 78, and 86. there is still a final examination, which counts as one grade.

a. in order to get an a, your average must be at least 90. if you get 100 on the final, compute your average and determine if an a in the course is possible.

b. to earn a b in the course, you must have a final average of at least 80. what must you get on the final to earn a b in the course?

Consider the following information on stocks a, b, c and their returns (in decimals) in each state: state prob. of state a b c boom 20% 0.27 0.22 0.16 good 45% 0.16 0.09 0.07 poor 25% 0.03 0 0.03 bust 10% -0.08 -0.04 -0.02 if your portfolio is invested 25% in a, 40% in b, and 35% in c, what is the standard deviation of the portfolio in percent? answer to two decimals, carry intermediate calcs. to at least four decimals.