The historical returns on a portfolio had an average return of
24 percent and a standard deviation of 31 percent. Assume that
returns on this portfolio follow a bell-shaped distribution.
a. Approximately what percentage of returns were greater
than 86 percent? (Round your answer to the nearest whole
percent.)
b. Approximately what percentage of returns were below –69
percent? (Round your answer to 1 decimal
place.)
Solution :
Given that ,
mean = = 24% = 0.24
standard deviation = = 31% = 0.31
(a) 86% = 0.86
P(x > 0.86) = 1 - P(x < 0.86)
= 1 - P((x - ) / < (0.86 - 0.24) / 0.31)
= 1 - P(z < 0.02)
= 1 - 0.508
= 0.492
Answer = 49%
(b)
-0.69% = -0.69
P(x < -0.69)
= P((x - ) / < (-0.69 - 0.24) / 0.31)
= P(z < -3)
= 0.0013
= 0.1%
Answer = 0.1%
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