Over the past four years,a stock produced returns of 14 percent,22 percent,6 percent,and −19 percent.What is the approximate probability that an investor in this stock will not lose more than 30 percent nor earn more than 41 percent in any one given year?
A)84 percent
B)95 percent
C)68 percent
D)5 percent
E)34 percent

Question

Quizplus · Accepted Answer

To find the probability that an investor will not lose more than 30% nor earn more than 41%, we need to find the range of returns that fall within this interval.

If we add/subtract 30% to/from each of the returns in the past four years, we get:

44%, 52%, 36%, and -49%

Now we need to find the probability that the return in any given year falls within the range of -30% to 41%.

Using the empirical rule, which states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations, we can estimate the probability.

If we assume that the returns are normally distributed, then the range -30% to 41% is approximately 1.5 standard deviations from the mean. Therefore, approximately 95% of the returns should fall within this range.

Thus, the approximate probability that an investor in this stock will not lose more than 30% nor earn more than 41% in any given year is 95%, making option B the best choice.

Over the Past Four Years,a Stock Produced Returns of 14