Given a business situation word problem or case study such as defective items or waiting lines, use discrete probability concepts to determine a course of action.

A company is interested in evaluating its current inspection process on shipments of 50 identical items. The process is to take a sample of 5 and pass the load if no more than two are found to be defective. What proportion of 20% of faulty shipments will be accepted?Use probability using Binomial Distribution: we will solve the business situation using the concept of discrete probability on an assembly line that is typically 3% defective a sample of 10 was taken and of the 10 exactly one was found to be defective . X~B(10 , 0.03)

The pdf of X P(X=x) = ( ) ( ) , x=0,1,2,.....,n P(X=x) = ( ) ( ) ( ) , x=0,1,2,.....,10 now

Find the probability of getting one or more defective items out of 10 P(X1)= 1- p(X<1) =1- p(X=0) =1-( ) ( ) ( ) = 1-0.737424 =0.262576 Therefore , with using the concept of discrete probability we could solve the business situation word problem.

include:

Calculate probabilities using binomial distribution.

Calculate the mean and standard deviation for a binomial distribution.

Calculate probabilities using Poisson distribution.

Calculate the mean and standard deviation for a Poisson distribution.

Show how times between arrivals can be modeled using Poisson distribution.