Unit 5: Binomial and Poisson Distributions

What are the excel functions for finding the binomial distribution probability?

1. BINOM.DIST(k,n,p,0) for P(X=k) 2. BINOM.DIST(k,n,p,1) for P(X is less than or equal to k). Ex if you calculate P(X is less than or equal to 5)=.0284, then there's a 2.8% chance that you have 5 or less successes in that sample n.

What is a Poisson distribution?

It's a model of counted data used when the count may go to infinity. The count represents the number of successes in a fixed unit of measure. (binomial dist. goes from 0 to n whereas poisson goes from 0 to infinity.) Assumptions of this distribution:

What are Binomial settings/distributions?

They're used to represent the number of successes in a series of n observations.The observations must meet the following conditions to be considered a binomial setting: 1. There are a fixed number of observations, n. 2. Each observation falls into one of the two categories: success of failure (binary). 3. The probability of success, p, is the same for each observation. The sample space of a binomial setting consists of 2^n possible outcomes. ex n=5 observations means 32 possible outcomes.

How can you approximate the population/binomial distribution and sample proportion with a normal distribution?

Check that the condition np is greater than or equal to 10 and n(1-p) is greater than or equal to 10 before using these.

How do you calculate the probability of a certain outcome occurring in a binomial setting?

P(outcome)= (p^n of successes)(1-p)^(n of failures) because P(FFSSF)=P(F)P(S)P(S)P(F) and P(F)=(1-p)

How does the binomial distribution equation change if we want to find the cumulative probability of k successes or less occurring?

Previously, P(X=k) but instead, P(X< or equal to k), which equals about: if np is greater than or equal to 10 and n(1-p) is greater than or equal to 10.

What is binomial distribution?

The distribution of the count X of successes in the binomial setting is the binomial distribution with parameters n and p. The possible values of X are whole numbers from 0 to n. Notation-wise, we write X is B(n,p). We also have Mu sub x= np and sigma sub x = square root of np(1-p)

What are Binomial and Poisson Distributions and what are they used to model?

They're discrete distributions and they model counts and proportions.