1. Graphs of Normal Probability Distributions The graph of a normal distribution is called a normal curve. It takes on the shape of a bell and is referred to as a bell curve.

2. Graphs of Normal Probability Distributions The graph of a normal distribution is called a normal curve. It takes on the shape of a bell and is referred to as a bell curve. Lets look at the properties of a bell curve :

3. Graphs of Normal Probability Distributions The graph of a normal distribution is called a normal curve. It takes on the shape of a bell and is referred to as a bell curve. Lets look at the properties of a bell curve : 1.The curve is bell shaped, with the highest point over the mean

4. Graphs of Normal Probability Distributions The graph of a normal distribution is called a normal curve. It takes on the shape of a bell and is referred to as a bell curve. Lets look at the properties of a bell curve : 1.The curve is bell shaped, with the highest point over the mean 2. The curve has symmetry about the mean

5. Graphs of Normal Probability Distributions The graph of a normal distribution is called a normal curve. It takes on the shape of a bell and is referred to as a bell curve. Lets look at the properties of a bell curve : 1.The curve is bell shaped, with the highest point over the mean 2. The curve has symmetry about mean 3. The curve approaches but never touches horizontal axis

6. Graphs of Normal Probability Distributions

9. The Empirical Rule : For a bell - shaped curve that is symmetrical

10. Graphs of Normal Probability Distributions The Empirical Rule : For a bell - shaped curve that is symmetrical - 68% of the data values lie within 1 standard deviation on either side of the mean 68% 34%

11. Graphs of Normal Probability Distributions The Empirical Rule : For a bell - shaped curve that is symmetrical - 68% of the data values lie within 1 standard deviation on either side of the mean - 95% of the data values lie within 2 standard deviations on either side of the mean 68% 34% 95% 13.5%

12. Graphs of Normal Probability Distributions The Empirical Rule : For a bell - shaped curve that is symmetrical - 68% of the data values lie within 1 standard deviation on either side of the mean - 95% of the data values lie within 2 standard deviations on either side of the mean - 99.7% of the data values lie within 3 standard deviations on either side of the mean 68% 34% 95% 13.5% 34% 99.7% 2.35%

13. Graphs of Normal Probability Distributions

16. 34%

17. Graphs of Normal Probability Distributions 34%

18. Graphs of Normal Probability Distributions

22. 34% 13.5%

23. Graphs of Normal Probability Distributions 34% 13.5%

24. Graphs of Normal Probability Distributions CONTROL CHARTS Control charts are used to examine data over a period of time intervals or in some sequential order. There exists an inherent amount of variability in any sequential data. A good example is the number of riders per hour on a roller coaster. That number will vary from hour to hour and day to day. Control charts combine graphic and numeric descriptions of data with probability distributions.

25. Graphs of Normal Probability Distributions

26. Day 123456789101112131415 11202523161982517202329181410

27. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410

28. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410

29. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410 19.3 28.7 33.4 9.9 5.2 Day RoomsRooms 1 2 3 4 5 6 7 8 9 10 11 12 1314 15

30. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410 19.3 28.7 33.4 9.9 5.2 Day RoomsRooms 1 2 3 4 5 6 7 8 9 10 11 12 1314 15

31. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410 19.3 28.7 33.4 9.9 5.2 Day RoomsRooms 1 2 3 4 5 6 7 8 9 10 11 12 1314 15

32. Graphs of Normal Probability Distributions Day 123456789101112131415 11202523161982517202329181410 19.3 28.7 33.4 9.9 5.2 Day RoomsRooms 1 2 3 4 5 6 7 8 9 10 11 12 1314 15

33. Graphs of Normal Probability Distributions

36. The probability of a false alarm = 0.003

37. Graphs of Normal Probability Distributions

38. The probability of a false alarm = 0.004

39. Graphs of Normal Probability Distributions

40. The probability of a false alarm = 0.002