Standard deviation of return on investment average probability

Question

in current year companies have an average return on investment of 12.8% and standard deviation of return is 3.2%. Average return is normally distributed. What is the probability that a random selected company in the market will have a return of investment that is within one standard deviation of the average of the return on investment in the market

Answer 1

For this you apply the empirical rule that states for a normal distribution 68% of the area under the normal curve is within 1 standard deviation of the mean, which equates to a 0.68 or 68% probability.