Z SCORES AND NORMAL CURVE DISTRIBUTIONS.ppt

NORMAL DISTRIBUTION CURVE

1. Z Scores & Normal Curves
Notes #3

2. What are Z-Scores?
ANS
Determines how many standard deviations
a raw score is from the mean.
The Z-score can be used to determine the
probability of an event occurring.

3. 2 Types of Z-Scores
1.Positive z-score, the data value lies
above the mean
2. Negative z-score, the data value lies below
the mean.

4. Z-Score Formula:
x
z




Symbols:
x : Raw score or number in question
Mean of the data set
Standard Deviation of the data set

5. Example 1
What is the z score for Iowa test score of 3.74,
with a mean of 6.84 and standard deviation of
1.55?
z = (3.74 – 6.84)/1.55
z = -2
FINAL ANS:
This says that a score of 3.74 is 2 standard deviation
BELOW the mean
x
z





7. •A set of math test scores has a mean
of 70 and a standard deviation of 8.
• A set of English test scores has a
mean
of 74 and a standard deviation of 16.
Ex. 2: Comparing the z-score data
For which test would a score of 78 have a higher standing?

8. Analyzing the data
To solve: Find the z-score for each test.
ANS: The score of 78 on the math test has a higher standing
since it is 1 standard deviation above the mean.
While a score of the 78 on the English score is only .25
standard deviation above the mean.

9. Ex. 3: Using Z-score to determine raw score
What will be the miles per gallon for a Toyota Camry
when the average mpg is 23, it has a z value of 1.5 and
a standard deviation of 5?
Using the formula for z-scores:
x
z




ANS: The Toyota Camry would be
expected to use 30.5 mpg of gasoline.
Step 1 Step 2 Step 3

10. Suppose SAT scores among college students are
normally distributed with a mean of 500 and a
standard deviation of 100. If a student scores a 700,
what would be her z-score?