Question

Assume the annual “profits” earned by mutual funds have a normal distribution with a mean of 8.6% and standard deviation 5.2%.

A. What is the probability a randomly selected mutual fund will have earned a positive profit?

B. What percent of mutual funds earned a profit between 2% and 18%?

C. The top 4% of mutual funds receive a AAA performance rating. What level of profit is needed to earn a AAA rating?

Answer 1

A) P(X > 0)

= P((X - )/ > (0 - )/)

= P(Z > (0 - 8.6)/5.2)

= P(Z > -1.65)

= 1 - P(Z < -1.65)

= 1 - 0.0495

= 0.9505

B) P(2 < X < 18)

= P((2 - )/ < (X - )/ < (18 - )/)

= P((2 - 8.6)/5.2 < Z < (18 - 8.6)/5.2)

= P(-1.27 < Z < 1.81)

= P(Z < 1.81) - P(Z < -1.27)

= 0.9649 - 0.1020

= 0.8629

c) P(X > x) = 0.04

or, P((X - )/ > (x - )/) = 0.04

or, P(Z > (x - 8.6)/5.2) = 0.04

or, P(Z < (x - 8.6)/5.2) = 0.96

or, (x - 8.6)/5.2 = 1.75

or, x = 1.75 * 5.2 + 8.6

or, x = 17.7