Question

QUESTION 4: The returns for an asset are normally distributed. The mean return is 9.75% and the standard deviation is 3.25%. a. What is the probability of earning a negative return? (3 points) b. What is the probability of earning a return between 6.5% and 16.25%? (3 points) c What is the probability of earning a return greater than 13%? (3 points)

Answer 1

Random variable X : Returns for an asset

Here mean = = 9.75% = 0.0975

Standard deviation = = 3.25% = 0.0325

a) P(earning negative return) = P(X < 0)

                                              

                                             

                                             =   P(z < -3)

                                            =   0.0013                      (From statistical table of negative z values)

Probability of earning a negative return = 0.0013

b) P(6.5% < X < 16.25%) = P(0.065 < X < 0.1625)

                                        

                                       

                                       = P(-1 < z < 2)

                                       = P(z < 2) - P(z < -1)

                                       = 0.9772 - 0.1587              (From statistical table of z values)

                                       = 0.8185

Probability of earning a return between 6.5% and 16.25% is 0.8185

c) P(X > 13%) = P(X > 0.13)

                      

                      

                       = P(z > 1)

                       = 1 - P(z < 1)

                       = 1 - 0.8413                      (From statistical table of z values)

                       = 0.1587

Probability of earning a return greater than 13% is 0.1587