1. Finding Percentages with z-scores
Normal Models
Finding Percentages with z-scores

2. z-scores
Z-scores standardize values to the standard Normal distribution N(0,1)
We can look up percentages when z-scores are not exactly 1, 2, or 3.
These are found on a table of Normal Percentiles or standard normal probabilities
This table is given to you on the AP Exam
The table always gives percentages from the z- score to negative infinite or left-tail probabilities

3. Using the Table Heights of young women. N(64.5, 2.5)
What percent of young women have a height of less than 60 inches?
Find z-score
Need to look up on the table.
Start by finding -1.8 on the left column.
Then go across to the first column for .00
Therefore 3.59% of young women
are shorter than 60 inches

4. Right Tail Percentages
What percentage of young women are taller than 63 inches?
Notation:
But this is for left tail, Total percent is 100% so subtract from 1
So 72.57% of young women are taller than 63 inches

5. Percents between
What percent of young women are between the heights of 59.5 and 65.5 inches?
Find both z-scores
Subtract two percentages
So 63.26% of young women are between 59.5 and inches.

6. Finding Value Given Percentage
At what height are the tallest 10% of young women?
Find z-score by finding closest percent on the table.
Looking for 90% since tallest is right tail
Closest is which is a z-score = 1.28
The tallest 10% of young women are taller than inches.

7. Calculator Tricks