6% is a possible annual return that is within one standard deviation from the mean. However, it is not the standard deviation. The standard deviation describes how much the possible actual returns vary (deviate) from the mean. 8% is a possible annual return that is within two standard deviations from the mean. However, it is not the standard deviation. The standard deviation describes how much the possible actual returns vary (deviate) from the mean. The standard deviation from the mean of the possible annual returns is within the range of the 68% confidence interval about the mean. The 68% confidence interval represents the range from one standard deviation on the left side of the mean to one standard deviation on the right side of the mean. The mean is 4%, and the range of possible results about the mean that falls within the 68% confidence interval is between 2% and 6%. 2% is 2% below the mean of 4%, and 6% is 2% above the mean of 4%. Thus, the standard deviation must be 2% (equal to the difference between 4% and 2% and also to the difference between 4% and 6%). This is confirmed by the 95.5% confidence interval. The 95.5% confidence interval represents the range from two standard deviations on the left side of the mean to two standard deviations on the right side of the mean. Since that interval is four percentage points on either side of the mean, one standard deviation must be half that, or 2 percentage points on either side of the mean. 4% is the mean of the normal distribution. It is not the standard deviation. The standard deviation expresses how much the possible actual returns vary (deviate) from the mean.
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