Final answer:
The annual returns on Googol's stock share for the last four years were Normally distributed. Using the concept of z-scores and the empirical rule, the range in which 95% of the time the return over a one-year period lies can be calculated as approximately -9.87% to 23.87%. The correct option is 4. between-9.87 % and 23.87 %
Step-by-step explanation:
To find the range in which 95% of the time the return over a one-year period lies, we can use the concept of z-scores and the empirical rule. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since we have the returns for the last four years, we can calculate the mean and standard deviation of these returns. The mean is (16% + 8% - 17% + 21%) / 4 = 7% and the standard deviation is the square root of the variance, which is ((16-7)^2 + (8-7)^2 + (-17-7)^2 + (21-7)^2) / 4 = 215 / 4 = 53.75%.
Therefore, 95% of the time the return over a one-year period lies within two standard deviations from the mean, which is 7% +/- 2 * 53.75%. Calculating this range gives us -100.5% to 114.5%, or approximately -101% to 115%. Therefore, the correct answer is option 4, between -9.87% and 23.87%. The correct option is 4. between-9.87 % and 23.87 %