Slides Prepared by JOHN S. LOUCKS St. Edwards University, 2002 South-Western/Thomson Learning,Chapter 6 Continuous Probability Distributions,Uniform Probability Distribution Normal Probability Distribution Exponential Probability Distribution,x,f(x),Continuous Probability Distributions,A continuous random variable can assume any value in an interval on the real line or in a collection of intervals. It is not possible to talk about the probability of the random variable assuming a particular value. Instead, we talk about the probability of the random variable assuming a value within a given interval. The probability of the random variable assuming a value within some given interval from x1 to x2 is defined to be the area under the graph of the probability density function between x1 and x2.,A random variable is uniformly distributed whenever the probability is proportional to the intervals length. Uniform Probability Density Functionf(x) = 1/(b - a) for a x b= 0 elsewherewhere: a = smallest value the variable can assumeb = largest value the variable can assume,Uniform Probability Distribution,Uniform Probability Distribution,Expected Value of xE(x) = (a + b)/2Variance of xVar(x) = (b - a)2/12where: a = smallest value the variable can assumeb = largest value the variable can assume,Example: Slaters Buffet,Uniform Probability DistributionSlater customers are charged for the amount of salad they take. Sampling suggests that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces.The probability density function isf(x) = 1/10 for 5 x 15= 0 elsewherewhere:x = salad plate filling weight,Example: Slaters Buffet,Uniform Probability DistributionWhat is the probability that a customer will take between 12 and 15 ounces of salad?,f(x),x,5,10,15,12,1/10,Salad Weight (oz.),P(12 x 20).,Standard Normal Probability DistributionThe Standard Normal table shows an area of .2967 for the region between the z = 0 and z = .83 lines below. The shaded tail area is .5 - .2967 = .2033. The probability of a stock-out is .2033. z = (x - )/ = (20 - 15)/6= .83,Example: Pep Zone,Using the Standard Normal Probability Table,Example: Pep Zone,Standard Normal Probability DistributionIf the manager of Pep Zone wants the probability of a stockout to be no more than .05, what should the reorder point be?Let z.05 represent the z value cutting the .05 tail area.,