The historical returns on a balanced portfolio have had an
average return of 13% and a standard deviation of 16%. Assume that
returns on this portfolio follow a normal distribution.
[You may find it useful to reference the z
table.]
a. What percentage of returns were greater than
45%? (Round your answer to 2 decimal
places.)
b. What percentage of returns were below −35%?
(Round your answer to 2 decimal places.)
Solution :
Given that ,
mean =
= 13% = 0.13
standard deviation =
= 16% = 0.16
a)
P(x > 45%) = 1 - P(x < 0.45)
= 1 - P((x -
) /
< (0.45-0.13) / 0.16)
= 1 - P(z <2 )
= 1 - 0.9772
= 0.0228
= 2.28%
Percetage = 2.28%
b)
P(x <-35% ) = P((x -
) /
< (-0.35-0.13) /0.16 )
= P(z <-3 )
= 0.0013
= 0.13%
Percentage = 0.13%
The historical returns on a balanced portfolio have had an average return of 13% and a...
Please provide simple explanation
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