Sampling Distributions - Concepts

The central limit theorem tells us

that if the sample size is sufficiently large, the distribution of x-bar will be approximately Normal with mean of mu and an SD of sigma/sqrt(n)

A fair die is rolled 12 times. X is the number of times an even number is rolled on the 12 rolls. What is the distribution of the mean X?

Binomial with mean of 6 (half of 12)

True or False: the probability of success for binomial distribution must remain the same for each observation

True

Binomial vs Poisson distributions

Both are for counts, but binomial is when the counts are set and Poisson when they can potentially be infinite

Conditions for using the Binomial distribution

• Each trial has exactly two outcomes

• Each trial is independent (one outcome doesn’t influence that of another).

• Probability of success p is the same for all trials.

• N, the sample size is fixed

Can you use the Normal distribution to estimate binomial probabilities? If so, when?

Yes when the sample size is very large

How do you calculate probabilities for x-bar? What about the Sum of x?

A probability calculator for both.

How do you differentiate a Central Limit Theorem problem vs Ch 1 problem? What about a sum problem?

Central Limit Theorem will refer to an average or mean. A sum problem will say sum or talk about the total of something.

What is the formula for SD for x-bar? And what is the mean?

Mean will be mu. SD will be sigma/sqrt(n)

What is the formula for mean and SD for sum of X?

N * mu. Sqrt(n * sigma)