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

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

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

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

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

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

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

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

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

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

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

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

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

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

Interpreting Z Example 6.2 Z = 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

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

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

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

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

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

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

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

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