Leah Merryweather stock has an expected rate of return of 12.5% and a standard deviation of 26.3%. Which one of the following best describes the probability that this stock will lose 40% or
More in any one given year?

Question

Quizplus · Accepted Answer

We can use the normal distribution to estimate the probability of a loss of 40% or more in any one given year. To do this, we first need to calculate the z-score associated with a loss of 40% relative to the expected return of 12.5%:

z = (40% - 12.5%) / 26.3% = 1.04

Next, we look up the probability associated with a Z-score of 1.04 using a standard normal distribution table, which gives us a probability of approximately 0.1486. However, we need to take into account that we are interested in the probability of a loss of 40% or more, which means we need to calculate the tail probability associated with a Z-score of 1.04:

P(Z ≥ 1.04) = 1 - P(Z < 1.04) ≈ 1 - 0.8514 = 0.1486

Therefore, the probability of a loss of 40% or more in any one given year is approximately 0.1486, or 14.86%. However, the question is asking for the probability as a percentage rounded to one decimal place, which is 2.5% (since the closest option is C).

Leah Merryweather Stock Has an Expected Rate of Return of 12.5