In: Statistics and Probability
The quarterly returns for a group of 59 mutual funds with a mean of 3.8% and a standard deviation of 6.9%
can be modeled by a Normal model. Based on the model
N(0.038,0.069), what are the cutoff values for the
a) highest 10% of these funds?
b) lowest 30%?
c) middle 20%?
d) highest 70%?
a) P(X > x) = 0.1
or, P((X - )/ > (x - )/) = 0.1
or, P(Z > (x - 0.038)/0.069) = 0.1
or, P(Z < (x - 0.038)/0.069) = 0.9
or, (x - 0.038)/0.069 = -1.28
or, x = -1.28 * 0.069 + 0.038
or, x = -0.05032
b) P(X < x) = 0.3
or, P((X - )/ < (x - )/) = 0.3
or, P(Z < (x - 0.038)/0.069) = 0.3
or, (x - 0.038)/0.069 = -0.52
or, x = -0.52 * 0.069 + 0.038
or, x = 0.00212
c) P(X < x) = 0.4
or, P((X - )/ < (x - )/) = 0.4
or, P(Z < (x - 0.038)/0.069) = 0.4
or, (x - 0.038)/0.069 = -0.25
or, x = -0.25 * 0.069 + 0.038
or, x = 0.02075
P(X > x) = 0.4
or, P((X - )/ > (x - )/) = 0.4
or, P(Z > (x - 0.038)/0.069) = 0.4
or, P(Z < (x - 0.038)/0.069) = 0.6
or, (x - 0.038)/0.069 = 0.25
or, x = 0.25 * 0.069 + 0.038
or, x = 0.05525
d) P(X > x) = 0.7
or, P((X - )/ > (x - )/) = 0.7
or, P(Z > (x - 0.038)/0.069) = 0.7
or, P(Z < (x - 0.038)/0.069) = 0.3
or, (x - 0.038)/0.069 = -0.52
or, x = -0.52 * 0.069 + 0.038
or, x = 0.00212