Unit 5 -Stat 2120

4 conditions that must be met to have observations considered a binomial setting

1. there are a fixed number of observations n 2. the n observations are all independent 3. each observation is binary: falls into 1 of two categories: success/failure 4. the probability of success p is the same for each observation

poisson distribution

models count data when the count (number of successes in a fixed unit of measure) may go to infinity

the Poisson probability will approximate the binomial probability where μ = np under what condition

n is large and p is small such that np < 10

Under what certain conditions does the sample proportion follow an approximate normal distribution?

np >= 10 AND n(1-p)>= 10

The number of students entering the library between 9 and 10am has a_________ distribution and In a manufacturing plant, 200 components are manufactured with known probability (0.1) of producing a defective component. The number of defective components, out of the 200 has a _______ distribution

poisson, binomial

If μ is the mean number of success per unit, then a * μ is, and aX is Poi(___)

the mean number of successes per a units, a*μ

binomial distributions

used to represent the # of successes in a series of n observations

binomial RV is where the random variable x=

where the random variable X = number of success in n observations

we can use normal approximation N(___, ____) to approximate poisson probabilities only when ___________

μ, sqrt μ, the mean is large

sample space of a binomial setting =

2^n possible outcomes

In a random sample of 20 students in a fitness study, X is the mean daily exercise time of the sample. X can be modeled using a binomial distribution. T/F? and why

False, bc the mean daily exercise time is one quantitative variable, and does not fall into one of 2 categoriesf

binomail distributions are used when we want to know _______________, not its ______

how often an event occurs, magnitude

Let x be the count of success in n observations. the sample proportion of successes is p-hat =

X/n

3 requirements for the poisson setting

1. # of successes that occur in two nonoverlapping units of measure are independent 2. probability that a success will occur in a unit of measure is the same for all units of equal size and is proportional to the size of the unit 3. probability that more than one event occurs in a unit of measure is negligible for very small-sized units (events occur one at a time)

the closer the mean is to ___ the more symmetric the poisson distribution

30

what is the notation of the poisson distribution , and the possible values of X are ____, and the RV x is equal to the __________

Poi(μ), whole numbers, number of successes in a poisson setting

distribution of the count X of success in binomial setting is____ and the possible values of X are _______ , notation of binomail distribution:

binomial distribution with parameters n and p, whole numbers from 0 to n, B(n, p)