Answer: 0.1587

## Explanation To solve this problem, we need to calculate the probability that the portfolio return exceeds 16% given a normal distribution with: - Mean (μ) = 9% - Standard deviation (σ) = 7% ### Step 1: Calculate the Z-score The Z-score measures how many standard deviations a value is from the mean: \[ Z = \frac{X - \mu}{\sigma} = \frac{16 - 9}{7} = \frac{7}{7} = 1 \] ### Step 2: Find the probability We want P(X > 16%), which is equivalent to P(Z > 1). From the standard normal distribution table: - P(Z ≤ 1) = 0.8413 - Therefore, P(Z > 1) = 1 - P(Z ≤ 1) = 1 - 0.8413 = 0.1587 ### Step 3: Interpretation This means there is a 15.87% probability that the portfolio return will exceed 16%. **Key Concept**: For a normal distribution, approximately: - 68% of values fall within ±1σ of the mean - 95% of values fall within ±2σ of the mean - 99.7% of values fall within ±3σ of the mean Since 16% is exactly 1 standard deviation above the mean, the probability of exceeding this value is the complement of the cumulative probability up to Z=1.

Author: Tanishq Prabhu