When returns from a project can be assumed to be normally distributed, such as those shown in Figure (represented by a symmetrical, bell-shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations. For example, 68.26 percent of the distribution will fall within one standard deviation of the expected value (± 1σ). Similarly, 95.44 percent will fall within two standard deviations ( ± 2σ), and so on. An abbreviated table of areas under the normal curve is shown next.

Assume Project A has an expected value of $24,000 and a standard deviation (σ) of $4,800.
a. What is the probability that the outcome will be between $16,800 and $31,200?
b. What is the probability that the outcome will be between $14,400 and $33,600?
c. What is the probability that the outcome will be at least $14,400?
d. What is the probability that the outcome will be less than $31,900?
e. What is the probability that the outcome will be less than $19,200 or greater than$26,400?

Number of 's from Expected Value 0.5 1.0 1.5 1.65 2.0 0.1915 0.3413 0.4332 0.4505 0.4772 +and 0.3830 0.6826 0.8664 0.9010 0.9544