Question

12. The stock market return data follow a normal distribution (Bell-Shape Curve). If the average annual return is 10%, and the standard deviation of annual returns is 15%, what conclusion could you draw on the possible returns over the next 100 years?

A. Approximately 68 out of 100 years, the returns will be greater than 10% but less than 15%.

B. Approximately 95 of out of 100 years, the returns will be greater than -20% but less than 40%.

C. Approximately 99 of out of 100 years, the returns will be greater than -20% but less than 40%.

D. Approximately 68 out of 100 years, the returns will be greater than -20% but less than 40%.

Answer 1

Given that

mean = 10

standard deviation = 15

using empirical rule, we know that

68% of data fall within 1 standard deviation of the mean =

95% of data fall within 2 standard deviation of the mean =

99.7% of data fall within 3 standard deviation of the mean =

option A, C and D are incorrect because given percentages are not matching with the calculated percentage returns.

so, only option B is correct