What is the probability that the return on the index in Example 5.8 will be below −15%?

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Example 5.8 Normal Distribution Function in Excel Suppose the monthly rate of return on the S&P 500 is approximately normally distributed with a mean of 1% and standard deviation of 6%. What is the probability that the return on the index in any month will be negative? We can use Excel's built-in functions to quickly answer this question. The probability of observing an outcome less than some cutoff according to the normal distribution function is given as NORM.DIST(cutoff, mean, standard deviation, TRUE). In this case, we want to know the probability of an outcome below zero when the mean is 1% and the standard deviation is 6%, so we compute NORM.DIST(0, 1, 6, TRUE) = .4338. We could also use Excel's built-in standard normal function, NORM.S.DIST, which uses a mean of 0 and a standard deviation of 1, and ask for the probability of an outcome 1/6 of a standard deviation below the mean: NORM.S.DIST(-1/6, TRUE) = .4338.