Chapter 3: Modeling Process Quality Flashcards
What is a probability distribution?
A mathematical model that relates the value of the variable with the probability of occurrence of that value in the population.
What are the two main types of distributions?
Continuous and Discrete
What are the characteristics of a hypergeometric distribution?
- Discrete
- Samples drawn from small populations without replacement –> once an item is chosen from the population, it cannot be chosen again.
- A particular item’s chance of being selected increases on each trial given that it has not yet been selected.
- Each item in the population is either an event or nonevent.
What are the charactersitics of a bionomial distribution?
Used to describe a process where the outcomes can be labeled as an event or nonevent if, for example, an item passes or fails inspection or a political party wins or loses. Often used in quality control, public opinion surveys, medical research, and insurance.
The number of events (X) in n trials follows a binomial distribution if the following conditions are met:
· The number of trials is fixed
· Each trial is independent
· Each trial has one of two outcomes: event or nonevent
· The probability of an event is the same for each trial
The binomial distribution is used when you are interested in the occurrence of an event and not in its magnitude. For example, you are interested in the number of defective items and not the degree of the defectiveness. Suppose a process produces 2% defective items. You are interested in knowing how likely is it to get 3 or more defective items in a random sample of 25 items selected from the process. The number of defective items (X) follows a binomial distribution with n = 25 and p = 0.02.
One of the properties of a binomial distribution is that when n is large and p is close to 0.5, the binomial distribution can be approximated by the standard normal distribution. For this graph, n = 100 and p = 0.5.
What’s the difference between binomial and hypergeometric distributions?
Both the hypergeometric distribution and the binomial distribution describe the number of times an event happens in a fixed number of trials. In the binomial distribution, trials are independent. For the hypergeometric distribution, each trial changes the probability for each subsequent trial because there is no replacement.
