Use the following information to calculate the standard deviation of Pirate Corporation's projected returns.

State of Economy Probability of State Occurring Rate of Return

Strong 0.3 20%

Normal 0.4 10%

Weak 0.3 5%

Standard deviation = 7.59

Explanation:

Standard deviation is the sum of the squared deviation of the individual return from the mean return under different scenarios

The mean return = ∑R*P

r - return under circumstance, P - probability

Mean return = (0.3*20%) + (0.4*10%) + (0.3*5%)

= 11.5%

Outcome R (R - r) ^2 P * (R - r) ^2

Strong 20 0.3 * (20-11.5) ^2 21.67

Normal 10 0.4 * (10-11.5) ^2 23.4

Weak 5 0.3 * (5%-11.5) ^2 2.67

57.75

Standard deviation = √57.75 = 7.59