Math Problem Statement

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 12.9% with a standard deviation of 16.7%. The relatively less risky fund promises an expected return and standard deviation of 4% and 6.7%, respectively. Assume that the returns are approximately normally distributed.

a-1. Calculate the probability of earning a negative return for each fund.

Note: Round your final answers to 4 decimal places. Calculate the probability of earning a return above 8.2% for each fund.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Normal Distribution
Z-scores

Formulas

Z = (X - μ) / σ
P(X < 0) and P(X > 8.2) based on Z-scores

Theorems

Normal Distribution Theorem
68-95-99.7 Rule

Suitable Grade Level

College/University Level - Finance/Statistics