A stock's return is normally distributed with a mean of 16% and a standard deviation of 8%. The probability that an investment in the stock will result in a loss in one year is approximately:
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A. B. C. D.B
Note that the mean is 2 standard deviations above zero. The probability that the stock's return will lie outside the 2-sigma range around the mean equals 5% for a standard normal distribution. This implies that the stock return will be either less than 0% or more than 32% with a 5% probability. Since the normal distribution is symmetrical about the mean, the probability that the stock return will be less than zero equals 5/2 = 2.5%. Instead of the above, you could also solve the problem using the z-score and the normal probability distribution table. You should, however, be aware of short-cuts like the above.