Question

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

(b)

-0.69% = -0.69

P(x < -0.69)

= P((x - ) / < (-0.69 - 0.24) / 0.31)

= P(z < -3)

= 0.0013

= 0.1%

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