1. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 1 The Normal Distribution

2. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 2 Properties of The Normal Distribution The curve is bell-shaped with the highest point over the mean, . 

3. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 3 Properties of The Normal Distribution The curve is symmetrical about a vertical line through . 

4. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 4 Properties of The Normal Distribution The curve approaches the horizontal axis but never touches or crosses it. 

5. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 5 Properties of The Normal Distribution The transition points between cupping upward and downward occur above  +  and  – .  –     

6. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 6 The Empirical Rule Approximately 68% of the data values lie is within one standard deviation of the mean. One standard deviation from the mean. 68%

7. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 7 The Empirical Rule Approximately 95% of the data values lie within two standard deviations of the mean. Two standard deviations from the mean. 95%

8. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 8 The Empirical Rule Almost all (approximately 99.7%) of the data values will be within three standard deviations of the mean. Three standard deviations from the mean. 99.7%

9. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 9 Section 6.1, Exercise 7: Assuming that the heights of college women are normally distributed with mean 65in. and standard deviation 2.5in., answer the following questions. (a)What percentage of women are taller than 65 in.? (b) What percentage of women are shorter than 65in.? (c) What percentage of women are between 62.5 in and 67.5in? (d) What percentage of women are between 60in. and 70in? Hint: use the empirical rule.

10. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 10 Example (similar to Section 6.1, Exercise 10). Suppose A vending machine automatically pours decaf coffee into 10oz capacity cups. It was found that the amount of decaf dispensed is normally distributed with a mean of 9.5 oz. and standard deviation of.25 oz. (a)Estimate the probability the machine will overflow the 10oz cup. (b) If the machine has been loaded with 1000 cups, how many do you expect will overflow when served? (c) If one thousand 9oz cups were mistakenly put in the dispenser, how many do you expect would not overflow when served?

11. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 11

12. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 12 Control Chart a statistical tool to track data over a period of equally spaced time intervals or in some sequential order

13. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 13 Statistical Control A random variable is in statistical control if it can be described by the same probability distribution when it is observed at successive points in time.

14. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 14 To Construct a Control Chart Draw a center horizontal line at . Draw dashed lines (control limits) at     and   . The values of  and  may be target values or may be computed from past data when the process was in control. Plot the variable being measured using time on the horizontal axis.

15. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 15 Control Chart      12345671234567

16. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 16 Control Chart      12345671234567

17. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 17 Out-Of-Control Warning Signals IOne point beyond the 3  level IIA run of nine consecutive points on one side of the center line at target  IIIAt least two of three consecutive points beyond the 2  level on the same side of the center line.

18. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 18 Probability of a False Alarm

19. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 19 Is the Process in Control?      12345671234567

20. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 20 Is the Process in Control?      1 2 3 4 5 6 7 8 9 10 11 12 13

21. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 21 Is the Process in Control?      12345671234567

22. Copyright (C) 2002 Houghton Mifflin Company. All rights reserved. 22 Is the Process in Control?      12345671234567