Returns of ?1.14% and below are outside the 99% confidence interval. However, this is not the probability that the return on the investment will be negative.
99% of the possible actual annual returns are expected to be between ?1.14% and 8%. That leaves 0.5% expected to be below ?1.14%, and 0.5% expected to be above 8%. However, the fact that 0.5% of the possible returns are expected to be below ?1.14% does not mean that 0.5% of the possible returns are expected to be negative. Any return below 0% is a negative return.
95.5% of the possible actual annual returns are expected to be between 0% and 8%. The remainder, or 4.5%, are expected to be either lower than 0% (negative returns) or higher than 8%. This 4.5% is divided equally between those lower than 0% and those higher than 8%. Since the question asks for the probability that the return on the investment will be negative, we are concerned here only with those possible returns that are lower than 0%. That is one-half of 4.5%, which is 2.25%.
95.5% of the possible actual returns are expected to be between 0% and 8%. 4.5% is the remainder, or 100% minus 95.5%. However, not all of the remaining 4.5% of the possible returns are expected to be negative (below 0%). This 4.5% remainder is divided equally between returns lower than 0% (negative returns) and those higher than 8%.
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What is the probability that the return on the Muggy-Day Industries investment will be negative?