Final answer:
The probability that a stock in Index A gained value in the year, given a mean return of 11.2% and considering the normal distribution of stock returns, is greater than 50%. However, the exact probability would normally be found using the z-score method and a normal distribution table, which requires a specific value to calculate the probability beyond the fact that returns are above zero.
Step-by-step explanation:
The question asks for the probability that a stock in Index A, which represents very large companies with a mean one-year return of 11.2% and a standard deviation of 19%, gained value in a given year. Given that the mean one-year return is already above 0%, and stock returns are approximately normally distributed, we can infer the probability of a gain is more than 50%. However, to provide a specific probability, we would typically use a z-score formula and a standard normal distribution table. Since the question only provides the mean and standard deviation, and no specific return value to calculate the z-score for, we presume the student wants to know the likelihood of any positive return, which can be estimated as the area under the normal distribution curve to the right of 0%. With a mean return of 11.2%, the z-score for 0% can be calculated using the formula: (0 - mean) / standard deviation = (0 - 11.2%) / 19%, resulting in a negative z-score, which indicates that the value zero is below the mean, and therefore the probability of a positive return is indeed greater than 50%.