Statistics 101 Ch. 5

Poisson distribution

A ________________ is a discrete probability distribution that applies to occurrences of some event over a specified interval. The random variable x is the number of occurances of the event in an interval.

Range Rule of Thumb

A main goal in statistics is to interpret and understand the meaning of statistical values. The ________ can be very helpful in understanding the meaning of mean and standard deviation.

A variable, x, that has a value for each outcome of the procedure, that is determined by chance.

Define random variable

1. Values of random var. 2. probabilities

Histogram from Prob. Dist.: 1. Horizontal Axis = ________ 2. Vertical Axis = __________

Values are unusual if they lie outside of: μ + 2σ & μ - 2σ If P(A) ≤ .05 , "A" is considered unusual.

How do you define usual or unusual values?

u = Σ [x*P(x)] P(x) = f/n

How do you find the Mean for probabilities?

σ^2 = Σ [x^2*P(x)] - Σu^2

How do you find the Variance for probabilities?

5% Guideline for Cumbersome Calculations

If calculations are time-consuming and if a sample size is no more than 5% of the size of the population, the _______ states to treat the selections as being independent (even if the selections are technically dependent)

Rare Event Rule.

If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. This represents the___________.

area and probability.

In a probability histogram, there is a correspondence between_______________.

number of successes

In the binomial probability formula, the variable x represents the__________.

expected value

The _____ of a discrete random variable represents the mean value of the outcomes.

x

____ represents the number of successes that occur in the n trials.

n

____ stands for the number of trials you are repeating.

q

____ stands for the probability of a failing outcome in a single trial.

p

____ stands for the probability of a successful outcome in a single trial.

P(x)

____ stands for the probability of getting "x" successes.

Probability distribution

__________ is a table that gives the probability for each value of a random variable.

Continuous random variable

__________ is a variable with an infinite number of possible values. (Typically related to a measurement)

Discrete Random Variable

___________ is a variable with a countable or finite number of values.

Binomial probability distribution.

_______________is a type of probability distribution that has only two outcomes: success and failure.

A random variable

________is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure.

1. The random variable x is the number of occurrences of an event over some interval. 2. The occurrences must be random 3. The occurrences must be independent of each other. 4. The occurrences must be uniformly distributed over the interval being used.

What are the requirements for a Poisson distribution?

1. Must be a fixed # of trials. 2. Trials must be independent. (The outcome of one trial does not effect any of the others,check against 5% guideline). 3. Each trial has only two outcomes. 4. The probability of success remains the same in all trials.

What are the rules for Binomial Probability Distributions?

Any number up to the number. ex: 0-8 satisfied "at most 8."

What does "at most" mean in statistics?

P(x) = n!/ (n-r)!x!*P^x*q^(n-x) or P(x) = nCx*p^x*q^(n-x)

What is the formula for Binomial Probability? (similar to combination formula)

P(x) = μ^x*e^-μ / x!

What is the formula for a Poisson distribution?

μ = n * p

What is the formula for mean (μ)

σ = √npq

What is the formula for standard deviation(σ)?

σ^2= n*p*q

What is the formula for variance(σ^2)?

The number of successes you expect to occur from your procedure.

What is the mean for a binomial distribution?

A)

Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability distributions? A) Use a simulation. B) Use a statistical table for binomial probabilities. C) Use computer software or a calculator D) Use the binomial probability formula.