AP STATISTICS
Chapter 2 – Exploring Data
Exploring the Basics
Day 3
A. Section 2.2
Name _______________________
Date __________
Period _____
Standard Normal Calculations
Key Vocabulary:
standard normal distribution, N(0,1), standardizing,
x
z-scores, z 
, standard normal table, assessing normality,

normal probability plot
Assignment: Exercises 2.21, 2.23, 2.24, 2.27
The standard normal curve – N(0,1) and
standard normal distribution
B. An infinite number of different normal density curves exist – one for each mean and standard deviation
combination.
To aid in calculating measurements of relative position (like percentiles), percentages, proportions and
probabilities, a technique called “standardizing” is used.
To “standardize” a value of a variable (x) from any N(  ,  ) we do the following calculation to get what is
known as the z-value or z score of the variable value:
z
x

; this value (z) measures the number of standard deviations above or below the mean.
B. Suppose the heights of the American 18 year old female population is N(64”,2).
What is the percentile of a young woman whose height is 66” ?
What proportion of the population has heights between 60” and 68” ?
There are 520 18 year old females in Lake Oswego. How many have heights less than 66” ?
C. What if the value of the variable is not at a “nice” spot? For instance, what is the percentile of a young
lady whose height is 64.5” ?
Steps: Find z-score.
Look up z-score on yellow packet standard normal table.
Determine percent.
Convert to percentile.
D. Working backwards! What is the z-score for Quartile 3? What is the height of this young lady?
Steps: Look up .7500 in body of table.
Identify the z-score.
Multiply z-score by size of standard deviation.
Add to mean.
E. Using the calculator to do C and D! Using the dist menu (2nd VARS) on your calculator.
normalcdf(LB,UB,mean,SD)
invnorm(.75)=.674 --- the z-score
normalcdf(0,64.5,64,2)=.5987 -- ~60th percentile
invnorm(.75,64,2)=65.3” --- the direct calculation
F. Assessing normality and the normal probability plot. The essence is: if the plot “shows” a fairly straight
line, there is more “density” in the middle, and there are no “outliers”, then we have an indication of
normality. Try this with Presidents data!