Over the past ﬁve years, a share produced returns of 14%, 22%, -16%, 2%, and 10%.What is the probability that an investor in this share will NOT lose more than 8% nor earn more than 21% in any
One given year?
A)34%
B)68%
C)95%
D)99%
E)100%

Question

Quizplus · Accepted Answer

To calculate the probability of the investor not losing more than 8% nor earning more than 21%, we have to find the range of returns between -8% and 21%. Therefore, we need to calculate the standard deviation of the given returns. 
Using the formula for standard deviation, we get:
Mean return (μ) = (14+22-16+2+10)/5 = 6.4%
Standard deviation (σ) = [ (14-6.4)^2 + (22-6.4)^2 + (-16-6.4)^2 + (2-6.4)^2 + (10-6.4)^2 ] / 5
= 16.96%
Now, we have to find the probability of the returns being between -8% and 21% with a mean return of 6.4% and a standard deviation of 16.96%. 
Using the standard normal distribution table, we can find the probability to be 0.68 or 68%. Therefore, the best choice is B.

Over the Past ﬁVe Years, a Share Produced Returns of 14