1. Chapter Six Normal Curves and Sampling Probability Distributions

2. Chapter 6 Section 1 Graphs of Normal Probability Distributions

3. Properties of The Normal Distribution The curve is bell-shaped with the highest point over the mean, .

4. Properties of The Normal Distribution The curve is symmetrical about a vertical line through .

5. Properties of The Normal Distribution The curve approaches the horizontal axis but never touches or crosses it.

6. Properties of The Normal Distribution The transition points between cupping upward and downward occur above  +  and  – .

7. The Empirical Rule Approximately 68.2% of the data values lie within one standard deviation of the mean.

8. The Empirical Rule Approximately 95.4% of the data values lie within two standard deviations of the mean.

9. Almost all (approximately 99.7%) of the data values will be within three standard deviations of the mean. The Empirical Rule

10. Percentages of data that lies between given values The Empirical Rule

11. Application of the Empirical Rule Variable 68.2% fall between 95.4% falls between 99.7% fall between Height of adult females 65”2.5” Contents of a box of cereal 20 oz.0.2 oz Life span of a battery 1000 hours50 hours Diameter of an engine part 3”0.05”

12. Application of the Empirical Rule The life of a particular type of light bulb is normally distributed with a mean of 1100 hours and a standard deviation of 100 hours. Question: What is the probability that a light bulb of this type will last between 1000 and 1200 hours? Answer: Approximately 0.6820

13. Application of the Empirical Rule The life of a particular type of light bulb is normally distributed with a mean of 1100 hours and a standard deviation of 75 hours. Question: What is the probability that a light bulb of this type will last between 950 and 1325 hours? Answer: Approximately 0.9755

14. Application of the Empirical Rule Answer: Approximately 0.3410

15. Application of the Empirical Rule Answer: Approximately 0.8180

16. Application of the Empirical Rule Answer: Approximately 0.0215

17. Application of the Empirical Rule Answer: Approximately 0.0230

18. Application of the Empirical Rule Answer: Approximately 0.0015

19. Control Chart A statistical tool to track data over a period of equally spaced time intervals or in some sequential order.

20. 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.

21. 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.

22. Control Chart     

23. Out-Of-Control Warning Signals I. One point beyond the 3σ level. II. A run of nine consecutive points on one side of the center line. III. At least two of three consecutive points beyond the 2σ level on the same side of the center line.

24. Is the Process in Control?     

25. Is the Process in Control?     

26. Is the Process in Control?     

27. Is the Process in Control?     

28. Is the Process in Control? Part 12345678910 Diameter (inches) 2.92.63.13.52.82.93.43.22.73.3

29. Is the Process in Control?     

30. Is the Process in Control? a.Do any points fall beyond the LCL and UCL three standard deviation limits? No points fall beyond the LCL and the UCL three standard deviations limit. Is there a run of nine consecutive points on one side of the center line? There is no run of nine consecutive points on one side of the center line. Is there an instance of two out of three points beyond the two standard deviation limits on the same side of the center line? There is no instance of two out of three points beyond the two standard deviation limits on the same side of the center line.

31. Uniform Probability Distributions

37. Exponential Probability Distributions

38. Uniform Probability Distributions

43. THE END OF SECTION 1 Homework Assignments Pages:259 - 266 Exercises: #1 - 19, odd Exercises: #2 - 20, even