5. Given the following probability distributions for Aspen Tech Inc. (ATI) and Sarasota Industrial (SI), answer the following questions:

State of Economy Probability ATI returns SI returns

Exceptional 20% 40% 22%

Average 50% 22% 8%

Recession 30% -15% 3%

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a) (12 points) What is the standard deviation for both ATI and SI?

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b) (4 points) Assuming a continuous distribution, approximately 95.46% of the time, the return for ATI will fall between _____ and _____.

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