1 1 Slide Continuous Probability Distributions n The Uniform Distribution  a b   n The Normal Distribution n The Exponential Distribution

2 2 Slide  a b The Uniform Probability Distributions The Uniform Probability Distributions  a b  a b x1x1 x2x2 x1x1 x1x1 P(x 1 ≤ x≤ x 2 ) P(x≤ x 1 ) P(x≥ x 1 ) P(x≥ x 1 )= 1- P(x<x 1 )

3 3 Slide The Uniform Probability Distribution n Uniform Probability Density Function f ( x ) = 1/( b - a ) for a < x < b f ( x ) = 1/( b - a ) for a < x < b = 0 elsewhere = 0 elsewherewhere a = smallest value the variable can assume b = largest value the variable can assume The probability of the continuous random variable assuming a specific value is 0. P(x=x 1 ) = 0

4 4 Slide The Normal Probability Density Function where  = mean  = mean  = standard deviation  = standard deviation  =  = e = e =

5 5 Slide The Normal Probability Distribution n Graph of the Normal Probability Density Function  x f ( x )

6 6 Slide The Standard Normal Probability Density Function where  = 0  = 0  = 1  = 1  =  = e = e =

7 7 Slide The table will give this probability Given any positive value for z, the table will give us the following probability Given positive z The probability that we find using the table is the probability of having a standard normal variable between 0 and the given positive z.

8 8 Slide Given z =.83 find the probability

9 9 Slide The Exponential Probability Distribution n Exponential Probability Density Function for x > 0,  > 0 for x > 0,  > 0 where  = mean e = e = n Cumulative Exponential Distribution Function where x 0 = some specific value of x

10 Slide The time between arrivals of cars at Al’s Carwash follows an exponential probability distribution with a mean time between arrivals of 3 minutes. Al would like to know the probability that the time between two successive arrivals will be 2 minutes or less. P ( x < 2) = /3 = =.4866 Example

11 Slide Example: Al’s Carwash n Graph of the Probability Density Function x x F ( x ) P ( x < 2) = area =.4866