1. Continuous Probability Distributions Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

2. Probability for a Continuous Random Variable Figure 6.1 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

3. Properties of a Normal Distribution Continuous Random Variable Symmetrical in shape (Bell shaped) The probability of any given range of numbers is represented by the area under the curve for that range. Probabilities for all normal distributions are determined using the Standard Normal Distribution. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

4. Probability Density Function for Normal Distribution Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

5. Figure 6.2 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

6. Figure 6.3 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

7. Figure 6.4 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

8. Figure 6.5 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

9. Figure 6.6 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

10. Determining the Probability for a Standard Normal Random Variable Figures 6.10-6.13 P(-  Z  1.62) =.5 +.4474 =.9474 P(Z > 1.62) = 1 - P(-  Z  1.62) = 1 -.9474 =.0526 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

11. Figure 6.10 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

12. Figure 6.11 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

13. Determining the probability of any Normal Random Variable Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing Fig 6.20

14. Interpreting Z Example 6.2 Z = - 0.8 means that the value 360 is.8 standard deviations below the mean. A positive value of Z designates how may standard deviations (  ) X is to the right of the mean (  ). A negative value of Z designates how may standard deviations (  ) X is to the left of the mean (  ). Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

15. Example 6.5 Referring to Example 6.2, after how many hours will 80% of the Evergol bulbs burn out? P(Z <.84) =.5 +.2995 =.7995 .8 Figure 6.26 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

16. Figure 6.26 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

17. Continuous Uniform Distribution The probability of a given range of values is proportional to the width of the range. Distribution Mean: Standard Deviation: Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

18. Figure 6.35 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

19. Figure 6.36 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

20. Exponential Distribution Applications: Time between arrivals to a queue (e.g. time between people arriving at a line to check out in a department store. (People, machines, or telephone calls may wait in a queue) Lifetime of components in a machine Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

21. Mean and Standard Deviation Mean: Standard Deviation: P ( X  x 0 )  1– e – Ax 0 for x 0  0 where A  1/ ,  = 1 A and  1 A. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

22. Figure 6.39 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing