Final answer:
Using the Empirical Rule and understanding of normal distribution, the probability of stock ABC earning a negative return is approximately 2.5%, based on its mean return of 10% and standard deviation of 5%.
Step-by-step explanation:
If stock ABC has a mean return of 10 percent with a standard deviation of 5 percent, then the probability of earning a negative return can be approximated using the concept of the normal distribution and z-scores. Since the mean return is 10%, a negative return would be a return less than 0%. To find the probability of getting a negative return, one would calculate the z-score of 0% with respect to the given mean and standard deviation. Using the empirical rule or z-table, we would determine the cumulative probability corresponding to this z-score.
However, without doing the calculations, we can apply the Empirical Rule as a quick approximation. Because the standard deviation is 5 percent and the mean is 10 percent, one standard deviation below the mean is 5 percent, and two standard deviations below the mean is 0 percent. So, the chance of getting a negative return (which lies below two standard deviations) is less than 2.5 percent of the time, according to the Empirical Rule which states that approximately 95 percent of the data falls within two standard deviations of the mean. Therefore, the correct answer is approximately: 2.5% (Option a).To find the probability of earning a negative return for stock ABC, we can use the standard normal distribution. Since the mean return is 10 percent and the standard deviation is 5 percent, we can calculate the z-score for a negative return.Z = (X - mean) / standard deviation = (0 - 10) / 5 = -2.Looking up the z-score in a standard normal table or using a calculator, we find that the probability of a z-score of -2 or lower is approximately 2.5 percent. Therefore, the answer is (a) 2.5%.