. The average return for large -cap domestic stock funds over the 3 years 2009-2011 was 14.4% (AAII Journal, February 2012). Assume the 3 year-year returns were normally distributed across funds with a standard deviation of 4.4%.a. What is the probability an individual large cap domestic stock fund had a 3 year return of at least 20%?b. What is the probability an individual large cap domestic stock fund had a 3- year return of 10% or less? c. How big does the return have to be to put a domestic stock fund in the top 10% for the 3- year period?

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Asked Jan 28, 2020
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. The average return for large -cap domestic stock funds over the 3 years 2009-2011 was 14.4% (AAII Journal, February 2012). Assume the 3 year-year returns were normally distributed across funds with a standard deviation of 4.4%.
a. What is the probability an individual large cap domestic stock fund had a 3 year return of at least 20%?
b. What is the probability an individual large cap domestic stock fund had a 3- year return of 10% or less?
c. How big does the return have to be to put a domestic stock fund in the top 10% for the 3- year period?

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Expert Answer

Step 1

(a)

The large-cap domestic stock funds over the three years are normally distributed with mean 14.4% and standard deviation 4.4%.

The probability that the three years return at least 20% is,

P(x≥20)

Software Procedure:

Step-by-step procedure to obtain the probability value using the Excel:

 

  • Use “=Norm.Dist(x, Mean, Standard deviation, Cumulative)”.
  • Type “=Norm.Dist(20,14.4,4.4,TRUE)”.

Output using the Excel is given below:

Statistics homework question answer, step 1, image 1
fullscreen
Step 2

From the output,

Statistics homework question answer, step 2, image 1
fullscreen
Step 3

Thus, the value of P(x≥20) is 0.1016.

(b)

The probability that the three years return is less than or equal to 10% is,

P(x≤10)

Software Procedure:

Step-by-step procedure to obtain the probability value using the Excel:

  • Use “=Norm.D...
Statistics homework question answer, step 3, image 1
fullscreen

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