Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent. What percent of investors at this brokerage house earned at least 5 percent?
A) 89.44 percent
B) 10.56 percent
C) 39.44 percent
D) 100 percent

Question

Quizplus · Accepted Answer

To find the percentage of investors who earned at least 5 percent, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (5 percent), $\mu$ is the mean (9 percent), and $\sigma$ is the standard deviation (3.2 percent). Plugging in the values, we get $Z = \frac{5 - 9}{3.2} = -1.25$. Looking up this Z-score in a standard normal distribution table or using a calculator, we find that the area to the left of this Z-score is approximately 10.56 percent, which means the area to the right (investors earning at least 5 percent) is 100 - 10.56 = 89.44 percent.

Suppose That It Is Believed That Investor Returns on Equity