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?

What does standard deviation measure in a portfolio?

How is standard deviation used to determine risk?

What is the difference between standard deviation and average deviation?

What is standard deviation used for in mutual funds?

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

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

What is the difference between standard deviation and mean?

A U.S. investor purchased some shares in Germany for 25 euros and sold them a year later for 42 euros

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

What is the difference between variance and standard deviation?

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

What is a relative standard error?

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

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

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

Are hedge funds regulated by FINRA?

Do financial advisors need to pass the Series 7 exam?

Is a financial advisor required to have a degree?

Do financial advisors need to be approved by FINRA?
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 ... 
What does standard deviation measure in a portfolio?
Dig deeper into the investment uses of, and mathematical principles behind, standard deviation as a measurement of portfolio ... 
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 the difference between standard deviation and average deviation?
Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ... 
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 ... 
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 ...
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. ... 
Residual Standard Deviation
A statistical term used to describe the standard deviation of ... 
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 ... 
ZScore
A ZScore is a statistical measurement of a score's relationship ...