Session 3: Quantitative Methods: Application Reading 9: Common Probability Distributions
LOS k: Determine the probability that a normally distributed random variable lies inside a given interval.
A stock portfolio has had a historical average annual return of 12% and a standard deviation of 20%. The returns are normally distributed. The range –27.2 to 51.2% describes a:
A) |
95% confidence interval. | |
B) |
68% confidence interval. | |
C) |
99% confidence interval. | |
The upper limit of the range, 51.2%, is (51.2 ? 12) = 39.2 / 20 = 1.96 standard deviations above the mean of 12. The lower limit of the range is (12 ? (-27.2)) = 39.2 / 20 = 1.96 standard deviations below the mean of 12. A 95% confidence level is defined by a range 1.96 standard deviations above and below the mean.
|