Betty is considering investing in a company's stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment.

Probability Return

Boom 0.3 25.00%

Good 0.4 15.00%

Level 0.1 10.00%

Slump 0.2 - 5.00%

a) What is hte expected return on Barbara's investment? (Round answer to 3 decimal places, e. g. 0.076) b) What is the standard deviation of the return on Barbara's investment? (Round answer to 5 decimal places, e. g. 0.07680)

a) What is the expected return on Barbara's investment?

0.135 or 13.5%

b) What is the standard deviation of the return on Barbara's investment?

0.04029 or 4.029%

Explanation:

Economy Probability Return

Boom 0.3 25.00% = 7.5%

Good 0.4 15.00% = 6%

Level 0.1 10.00% = 1%

Slump 0.2 - 5.00% = - 1

total 0.135 or 13.5%

0.075

0.06

0.01

-0.01

.135 / 4 = 0.03375 mean

0.075 - 0.03375 = 0.04125² = 0.001701562

0.06 - 0.03375 = 0.02625² = 0.000689062

0.01 - 0.03375 = - 0.02375² = 0.000564062

-0.01 - 0.03375 = - 0.04375² = 0.00191406

0.00486875

0.00486875 / (4 - 1) = 0.00486875 / 3 = 0.001622916

√0.001622916 = 0.04029