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# Statistics: The annual returns on US corporate stock

Subject: Mathematics    / Statistics
Question

4.36 The annual returns on US corporate stock and US Treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with US corporate stock having a mean of 15 percent and standard deviation of 20 percent, and US Treasury bonds having a mean of 6 percent and standard deviation of 9 percent. Which asset is more likely to have a negative return? Explain your reasoning.

4.37In his 1868 work, Carl Wunderlich concluded that temperatures above 100.4
Fahrenheit should be considered feverish. In a 1992 study, Maryland researchers
suggested that 99.9 Fahrenheit was a more appropriate cutoff [28]. If the oral
temperatures of healthy humans are normally distributed with a mean of 98.23
and a standard deviation of 0.67 (values estimated by the Maryland researchers),
what fraction of these readings are above 100.4? Above 99.9?

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