Final answer:
To find the probability, calculate the z-score of a -33.3% return given a mean return of 13.9% and a standard deviation of 23.3%. Check the z-score in a standard normal distribution table to find the probability.
Step-by-step explanation:
The question asks about the probability that a stock with an expected rate of return of 13.9 percent and a standard deviation of 23.3 percent will lose more than 1/3 of its value in any one year. To answer this, we can assume a normal distribution of stock returns and use the z-score formula to find how many standard deviations away a 33.3% loss is from the expected return.
Calculating the Z-score
The z-score is calculated as (X - μ) / σ, where X is the value of interest, μ is the mean (expected return), and σ is the standard deviation. We want to find the z-score for a -33.3% return when the expected return (μ) is 13.9% and the standard deviation (σ) is 23.3%. Subtracting 33.3% from 13.9% and then dividing by the standard deviation gives us the z-score.