Chapter 6 Notes
Normal Distribution (Continued)
The heights of De Anza women students are
approximately normally distributed with a mean
of 65 inches and a st dev of 3 inches.
X ~ N(65, 3)
3. Find the middle 50% of De Anza women’s
heights.
4. 30% of all De Anza women are taller than
how many inches?
Z-scores
A z-score tells us how many standard deviations
a data value x is from the mean.

z  x
Example: Given X~N(27,5)
data value x
17
27
32
20
z-score z
z=2.3
The closer a z-score is to 0, the closer x is to the
mean μ.
The Standard Normal Distribution
Suppose I have a population which is normally
distributed.
If I calculated a z-score for each of the members of
the population, then the z-scores will also be normally
distributed, with a mean   0 and standard deviation
 1
This is called the Standard Normal Distribution and its
distribution is written:
The Standard Normal Distribution is used to compare
normally distributed populations that have different
parameters.