High School

Last year, the rates of return on the common stocks in a large portfolio had an approximately mound-shaped distribution, with a mean of 20% and a standard deviation of 10%. Use the empirical rule to answer the following questions. 1. What proportion of the stocks had a return of between 10% and 30%? 68.3 % (to 1 decimal) 2. What proportion of the stocks had a return that was either less than 10% or more than 30%? 31.7 % (to 1 decimal) 3. What proportion of the stocks had a positive return? 97.5 % (to 1 decimal) 4. What proportion of the stocks had a return of between - 10% and 40%? 97.6 % (to 2 decimals)

Answer :

Final answer:

The empirical rule can be used to estimate the proportions of returns within different ranges in a normal distribution.

Explanation:

The empirical rule, also known as the 68-95-99.7 rule, is used to estimate the proportion of data within a certain range in a normal distribution. For the given portfolio, with a mean rate of return of 20% and a standard deviation of 10%, we can apply the empirical rule:

  1. Between 10% and 30%: This range is within one standard deviation of the mean, so approximately 68.3% of the stocks in the portfolio would have returns within this range.
  2. Less than 10% or more than 30%: The stocks outside the range of one standard deviation from the mean would account for approximately 31.7% of the total stocks.
  3. Positive return: Since the mean is 20% (positive), we can estimate that approximately 97.5% of the stocks in the portfolio had a positive return.
  4. Between -10% and 40%: This range is within two standard deviations of the mean, so approximately 97.6% of the stocks in the portfolio would have returns within this range.

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