Name:
2.2 Notetaking Guide
AP Statistics
Standardized Scores
What is a z-score?
Why do we Standardize?
EXAMPLE: The Virginia Cooperative Extension reports that
the mean weight of yearling Angus steers is 1152
points. Suppose that weights of all such animal can be
described by a NORMAL model with a standard deviation of
84 pounds.
How many standard deviations from the mean would a steer
weighing 1000 pounds be?
The z-chart! Where are the blue sheets?
Using the table to find
percentages from z-scores
Find P(z < -1.46)
Find P(z > -1.46)
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152
points. Suppose that weights of all such animal can be described by a Normal model with a standard
deviation of 84 pounds.
What proportion of the steers would weigh less than 1000 pounds?
Which would be more unusual, a steer weighing 1000 pounds or a steer weighing 1250
pounds?
Using the table to find z-scores from percentages
In a standard normal model, what value(s) of z cut(s) off the region described? DRAW A PICTURE.
The highest 20%
The highest 75%
The lowest 3%
The middle 90%
EXAMPLE
Scores on the SAT verbal test in recent years follow approximately the normal distribution, with mean
of 505 and sd 110. How high must a student score in order to place in the top 10% of all students
taking the SAT?
FINDING PROPORTION OF SCORES ABOVE,
BELOW, OR BETWEEN Z-SCORES
NORMAL PROBABILITY PLOT
GIVEN THE PROPORTION OF SCORES
BELOW A VALUE, FIND Z-SCORE.