Sec. 7-5: Central Limit Theorem

This theorem allows us to make corrections to the standard deviation (σ) because of errors acquired through sampling SAMPLES. In other words, the information we will now be given deals with only PART of a population. P(x compared to a value) The larger the sample is, the more normally distributed the data will be.

We will use 2 possible corrections for the σ, they are as follows. Standard Error of the Mean: use when n ≥ 30. σx = σ √n

Use when n < 30 or n > .05N Finite Population Correction Factor: Use when n < 30 or n > .05N Where n is the sample size & N is the population size. σx = σ · √N – n √n N – 1

One of these 2 correction factors will now be used in the z-score formula for “σ”. Z = x – μ σx So again, we will now be finding the probability of the MEAN OF A SAMPLE. P(x) = .****