Answer:
A) The assessment does not follow a normal distribution
B ) P(r<0) = 0.2546 ( from standard normal table ), P( r > 0.16 ) ≠ 0.15
Explanation:
Expected return on portfolio E (r) = 8%
Standard deviation (STD) = 12%
chances of Negative return P(r < 0 ) = 25%
calculate the probabilities for a normal distribution
E (r) = 0.08 , STD = 0.12, P(r < 0 ) = 0.25
P( r > 0.16 ) = 0.15
calculating the value of the probability P(r < 0 )
P(r < 0 ) = P [tex](Z < \frac{0-E(r)}{STD} )[/tex]
= P ( Z < [tex]\frac{0-0.08}{0.12}[/tex] )
= P ( Z < - 0.667 )
P(r<0) = 0.2546 ( from standard normal table )
calculating the value of the probability P( r > 0.16 )
P( r > 0.16 ) = [tex]P ( Z > \frac{0.16- E(r)}{STD})[/tex]
= P ( Z > [tex]\frac{0.16-0.08}{0.12}[/tex] )
= P ( Z > 0.667 )
to compare if p(r>0.16 ) is = 0.15
P(R > 0.16 ) = 1 - P ( Z < 0.667 )
= 1 - 0.7454 ( value from standard normal table )
= 0.2546
hence P( r > 0.16 ) ≠ 0.15
The assessment does not follow a normal distribution
