Page 82 - FINAL CFA SLIDES DECEMBER 2018 DAY 3
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Session Unit 3:
10. Common Probability Distributions
LOS 10.l: Define the standard normal distribution, explain how to standardize a RV, and calculate and
interpret probabilities using the standard normal distribution, p.226
The standard normal distribution is a ND that is standardized so that it has a mean of zero and
a SD= 1 [i.e., N~(0,1)]. Standardization is the process of converting an observed value for a
random variable to its z-value. Formally stated as
Example: Standardizing a random variable (calculating z-values). Assume that the annual
earnings per share (EPS) for a population of firms are normally distributed with a mean of
$6 and a standard deviation of $2. What are the z-values for EPS of $8 and $2?
Answer: If EPS = x = $8, then z = (x – μ) / σ = ($8 – $6) / $2 = +1
Meaning?
If EPS = x = $2, then z = (x – μ) / σ = ($2 – $6) / $2 = –2
At z = +1, EPS of $8 is 1 SD above the mean.
At z = –2, EPS of $2 is 2 SD below the mean.
We could use CDF F(x) = F(Z) (p.345/6) to derive p of observing z value less than a given value!
Importance?
