1. Z Score
The z value or z score tells the number of standard deviations the original measurement is from the mean.
The z value is in standard units.

2. Formula for z score

3. Calculating z-scores
The amount of time it takes for a pizza delivery is approximately normally distributed with a mean of 25 minutes and a standard deviation of 2 minutes. Convert 21 minutes to a z score.

4. Calculating z-scores
Mean delivery time = 25 minutes Standard deviation = 2 minutes
Convert 29.7 minutes to a z score.

5. Interpreting z-scores The delivery time is 28.2 minutes.
Mean delivery time = 25 minutes Standard deviation = 2 minutes
Interpret a z score of 1.6.
The delivery time is 28.2 minutes.

6. Standard Normal Distribution:
 = 0
 = 1 -1 1
Values are converted to z scores where z =

7. Importance of the Standard Normal Distribution:
Any Normal Distribution: 1
Areas will be equal.  1

8. Use of the Normal Probability Table
(Table 5) - Appendix II
Entries give the probability that a standard normally distributed random variable will assume a value to the left of a given negative z-score.

9. Use of the Normal Probability Table
(Table 5a) - Appendix II
Entries give the probability that a standard normally distributed random variable will assume a value to the left of a given positive z value.

10. To find the area to the left of z = 1.34
_____________________________________ .
1.2 … ….
1.3 … ….
1.4 … ….

11. Patterns for Finding Areas Under the Standard Normal Curve
To find the area to the left of a given negative z :
Use Table 5 (Appendix II) directly. z

12. Patterns for Finding Areas Under the Standard Normal Curve
To find the area to the left of a given positive z :
Use Table 5 a (Appendix II) directly. z

13. Patterns for Finding Areas Under the Standard Normal Curve
To find the area between z values on either side of zero:
Subtract area to left of z1 from area to left of z2 . z2 z1

14. Patterns for Finding Areas Under the Standard Normal Curve
To find the area between z values on the same side of zero:
Subtract area to left of z1 from area to left of z2 . z1 z2

15. Patterns for Finding Areas Under the Standard Normal Curve
To find the area to the right of a positive z value or to the right of a negative z value:
Subtract from the area to the left of the given z.
Area under entire curve = z

16. Use of the Normal Probability Table
a. P(z < 1.24) = ______
b. P(0 < z < 1.60) = _______
c. P( < z < 0) = ______
.8925
.4452
.4911

17. Normal Probability d. P( - 3 < z < 3 ) = ________
.9974
d. P( - 3 < z < 3 ) = ________
e. P( < z < 1.57 ) = _____
f. P( 1.24 < z < 1.88 ) = _______
.9322
.0774

18. Normal Probability g. P( - 2.44 < z < - 0.73 ) = _______
.2254
g. P( < z < ) = _______
h. P( z < 1.64 ) = __________
i . P( z > 2.39 ) = _________
.9495
.0084

19. Normal Probability j. P ( z > - 1.43 ) = __________
k. P( z < ) = __________
.9236
.0034

20. Application of the Normal Curve
The amount of time it takes for a pizza delivery is approximately normally distributed with a mean of 25 minutes and a standard deviation of 2 minutes. If you order a pizza, find the probability that the delivery time will be: a. between 25 and 27 minutes. a. ___________ b. less than 30 minutes. b. __________
c. less than 22.7 minutes. c. __________
.3413
.9938
.1251