Q:
A:
XYZ Company stocks have an expected return of 12% and a standard deviation of 8%. Assuming that the returns of this company are a continuous random variable that is normally distributed, what is the probability that the returns will be 1.2% or less?
A) 45%
B) 1.65%
C) 10%
D) 5%
A) 45%
B) 1.65%
C) 10%
D) 5%
The correct answer is: D)
First, transform the actual value of this outcome (1.2%) into its standardized zscore:
Z_{x}= [(X  u_{x}) ÷ σ_{x}] = [(1.2  12.0) ÷ 8] = 1.65
Using the Normal Rule, candidates should realize that approximately 90% of the outcomes are expected to occur within 1.65 standard deviations of the mean. This would mean that 45% (half of 90%) of the observations must lie within the mean and 1.65 standard deviations away from the mean. If this is so, then 5% of all the observations must lie below 1.65 standard deviations away from the mean.
MORE FAQS

What is the difference between standard deviation and z score?

How is standard deviation used to determine risk?

What is standard deviation used for in mutual funds?

How is risk aversion measured in Modern Portfolio Theory (MPT)?

What is the difference between the expected return and the standard deviation of a portfolio?

What is the difference between variance and standard deviation?

Stock A has a standard deviation of 16% and a beta of 1.1 ...

What two components are used to calculate riskadjusted return? I ...

What can the coefficient of variation (COV) tell investors about an investment's volatility?

What is a double Bollinger Bands® strategy?

How can an investor use the ZScore to compare investment options?

What does a ZScore tell a stock analyst about the health of a company?

How is the Altman ZScore used in fundamental analysis?

How can you calculate volatility in Excel?

How does my insurance company determine what premiums I have to pay for coverage?

How many attempts at each CFA exam is a candidate permitted?

Do financial advisors need to pass the Series 7 exam?

Do financial advisors need to be approved by FINRA?

How does a broker decide which customers are eligible to open a margin account?

Why is the Nasdaq more heavily weighted to tech stocks than other stock exchanges?
RELATED FAQS

What is the difference between standard deviation and z score?
Understand the basics of standard deviation and Zscore; learn how each is calculated and used in the assessment of market ... 
How is standard deviation used to determine risk?
Understand the basics of calculation and interpretation of standard deviation and how it is used to measure risk in the investment ... 
What is standard deviation used for in mutual funds?
See how standard deviation is helpful in evaluating a mutual fund's performance. Use it in combination with other measurements ... 
How is risk aversion measured in Modern Portfolio Theory (MPT)?
Find out how risk aversion is measured in modern portfolio theory (MPT), how it is reflected in the market and how MPT treats ... 
What is the difference between the expected return and the standard deviation of ...
Learn about the expected return and standard deviation and the difference between the expected return and standard deviation ... 
What is the difference between variance and standard deviation?
Explore the differences between standard deviation and variance. Learn more about how statisticians use these two concepts.
RELATED TERMS

Empirical Rule
A statistical rule stating that for a normal distribution, almost ... 
Standard Deviation
1. A measure of the dispersion of a set of data from its mean. ... 
Standard Error
The standard deviation of the sampling distribution of a statistic. ... 
Downside Risk
An estimation of a security's potential to suffer a decline in ... 
Downside Deviation
A measure of downside risk that focuses on returns that fall ... 
Expected Return
The amount one would anticipate receiving on an investment that ...