The quarterly returns for a group of 54 mutual funds with a

The quarterly returns for a group of 54 mutual funds with a mean of 4.1% and a standard deviation of 5.3% can be modeled by a Normal model. Based on the model N(0.041,0.053), what are the cutoff values for the

a) highest 30% of these funds? b) lowest 40%? c) middle 60%? d) highest 60%?

Solution

a)
P ( Z > x ) = 0.3
Value of z to the cumulative probability of 0.3 from normal table is 0.52
P( x-u/ (s.d) > x - 0.041/0.053) = 0.3
That is, ( x - 0.041/0.053) = 0.52
--> x = 0.52 * 0.053+0.041 = 0.0688                  

b)
P ( Z < x ) = 0.4
Value of z to the cumulative probability of 0.4 from normal table is -0.253
P( x-u/s.d < x - 0.041/0.053 ) = 0.4
That is, ( x - 0.041/0.053 ) = -0.25
--> x = -0.25 * 0.053 + 0.041 = 0.0276                  

d
P ( Z > x ) = 0.6
Value of z to the cumulative probability of 0.6 from normal table is -0.25
P( x-u/ (s.d) > x - 0.041/0.053) = 0.6
That is, ( x - 0.041/0.053) = -0.25
--> x = -0.25 * 0.053+0.041 = 0.0276