Final answer:
To find the 95% confidence interval of the annual returns, we calculate the mean and an estimated standard deviation and apply the empirical rule. The estimated range is between -12% and 26%, but since the given returns are between -17% and 21%, the closest range is between -17% and 21%.
Step-by-step explanation:
The student is asking about a statistical concept related to the normal distribution of annual returns on stock shares. When dealing with normally distributed data, we often use empirical rule which states that approximately 95% of the data falls within two standard deviations of the mean. To answer this question, we need to calculate the mean (average) and standard deviation of the given returns.
The mean return is calculated as the sum of all returns divided by the number of returns. So, the mean return is (16% + 8% - 17% + 21%) / 4 = 7%. The standard deviation can be approximated by finding the range of values and dividing it by 4, as the returns are somewhat evenly spread out and a small sample size is given. The difference between the highest and lowest return is 21% - (-17%) = 38%. Dividing this by 4 gives us a standard deviation of approximately 9.5%.
Now, 95% of the data falls within two standard deviations of the mean. Therefore, the range can be estimated as 7% ± (2 * 9.5%) = [7% - 19%, 7% + 19%] = [-12%, 26%]. However, since the actual lowest and highest given returns are -17% and 21%, respectively, the closest answer choice to our calculated range that includes all the given data points is between -17% and 21%.