Question

Suppose that a group of mutual funds had an average return of 2% last year with a standard deviation of 3.6%. Assume these funds are normally distributed. What is the probability that a randomly selected fund had a positive return last year?

Answer 1

Solution:

Given: a group of mutual funds had an average return of 2% last year with a standard deviation of 3.6%.

Find:

P(  a randomly selected fund had a positive return last year) =.................?

That is find:

P( X > 0% )= ..............?

Find z score for x = 0%

thus we get:

P( X > 0% )= P( Z > - 0.56 )

P( X > 0% )= 1 - P( Z < - 0.56 )

Look in z table for z = -0.5 and 0.06 and find corresponding area.

P( Z< -0.56)= 0.2877

thus

P( X > 0% )= 1 - P( Z < - 0.56 )

P( X > 0% )= 1 -0.2877

P( X > 0% )= 0.7123

Thus P( a randomly selected fund had a positive return last year) = 0.7123