1. WASC NEXT WEEK! Warm-Up… Quickwrite…
The WASC team is a group of people who will observe the school to see how it is functioning. What changes do you think need to be made in this class when the WASC team visits?
Ex: “When the WASC team visits, I think this class needs to _______ ___________ because ____________________________________.”

2. Compare and Explain… your Warm-Up starting with Student #1 (1 min) 50%
68%
95%

3. Round Robin…
starting with the student who sat down first at your table today (1 min)
The WASC team is a group of people who will observe the school to see how it is functioning. What changes do you think need to be made in this class when the WASC team visits?
Ex: “When the WASC team visits, I think this class needs to _______ ___________ because ____________________________________.”

5. z scores & raw scores

6. For Normal Distributions…
It would be a futile task to try to set up a table of areas under the normal curve for each different  and  combination
We need a way to standardize the distributions so that we can use one table of areas for all normal distributions
We achieve this standardization by considering how many standard deviations a measurement lies from the mean
In this way, we can compare a value in one normal distribution with a value in another, different normal distribution

7. Example
Suppose Tina and Jack are in two different large sections of the same course
The scores on the midterm exams of each section follow a normal distribution
Tina’s section: the average (mean) was 64 and her score was 74
Jack’s section: the mean was 72 and his score was 82
Both Tina and Jack were pleased that their scores were each 10 points above the average of each respective section
But the fact that each was 10 points above average does not really tell us how each did with respect to the other students in the section

8. Tina’s 74 was higher than most of the other scores in her section; Jack’s 82 is only an upper-middle score in his section
Tina’s score is far better with respect to her class than Jack’s score is with respect to his class

9. The previous example…
demonstrates that it is not sufficient to know the difference between a measurement (x value) and the mean of a distribution
We need also to consider the spread of the curve, or the standard deviation
What we really want to know is the number of standard deviations between a measurement and the mean, which takes both  and  into account

10. z Scores
We can use a simple formula to compute the number z of standard deviations between a measurement x and the mean  of a normal distribution with standard deviation 

11. z Scores
The mean is a special value of a distribution; when we convert x =  to a z value:
The mean of the original distribution is always zero, in standard units
This makes sense because the mean is zero standard variations from itself

12. z Scores
An x value in the original distribution that is above the mean  has a corresponding z value that is positive
Likewise, an x value below the mean has a negative z value
x Values and Corresponding z Values

13. Example
A pizza parlor franchise specifies that the average (mean) amount of cheese on a large pizza should be 8 ounces and the standard deviation only 0.5 ounce
An inspector picks out a large pizza at random in one of the pizza parlors and finds that it is made with 6.9 oz. of cheese
Assume that the amount of cheese on a pizza follows a normal distribution
If the amount of cheese is below the mean by more than 3 standard deviations, the parlor will be in danger of losing its franchise

14. Example
How many standard deviations from the mean is 6.9? Is the pizza parlor in danger of losing its franchise?
Since we want to know the number of standard deviations from the mean, we want to convert 6.9 to standard z units
The amount of cheese is only 2.20 standard
deviations from the mean
The parlor will not lose its franchise

15. What is a Raw Score?