Question

the average return for large-cap domestic stock funds over the three years 2009–2011 was 14.9%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.1%. Use Table 1 in Appendix B.

a. What is the probability an individual large-cap domestic stock fund had a three-year return of at least 20% (to 4 decimals)?

b. What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less (to 4 decimals)?

c. How big does the return have to be to put a domestic stock fund in the top 10% for the three-year period (to 2 decimals)?
  %

Answer 1

a)

The following information has been provided:

μ=14.9, σ=4.1

We need to compute Pr(X≥20). The corresponding z-value needed to be computed is:

Therefore, we get that

The following is obtained graphically:

b)

The following information has been provided:

μ=14.9, σ=4.1

We need to compute Pr(X≤10). The corresponding z-value needed to be computed:

Therefore,

The following is obtained graphically:

c)

The following information has been provided:

μ=14.9, σ=4.1

We need to compute x such that P(X>x) = 0.10

Therefore, we get that

The following is obtained graphically:

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