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The mean of 1,000 quarterly returns is calculated as 4.52%. The standard deviation of these returns is calculated as 1.84%. An investor can be 95% certain that the return for any particular quarter will be at least:

Question

The mean of 1,000 quarterly returns is calculated as 4.52%. The standard deviation of these returns is calculated as 1.84%. An investor can be 95% certain that the return for any particular quarter will be at least:

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Solution

To answer this question, we need to understand the concept of a confidence interval in statistics. A 95% confidence interval is defined as a range of values such that with 95% probability, the range will contain the true unknown value of the parameter. In a normal distribution, a 95% confidence interval corresponds to a range that is 1.96 standard deviations away from the mean on both sides.

Here are the steps to calculate it:

  1. Calculate the standard deviation range: Multiply the standard deviation by 1.96. In this case, 1.84% * 1.96 = 3.6064%.

  2. Subtract this range from the mean to get the lower bound of the confidence interval. In this case, 4.52% - 3.6064% = 0.9136%.

So, an investor can be 95% certain that the return for any particular quarter will be at least 0.9136%.

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