Section VII, Measure - Probability. Central Limit Theorem. States that any distribution of sample means from a large population approaches the normal distribution as n increases to infinity The mean of the population of means is always equal to the mean of the parent population.
Central Limit Theorem Explanation
For almost all populations, the sampling distribution of the mean can be closely approximated by a normal distribution, provided the sample is sufficiently large.
Collect many x children, (assumption is infinite number of samples), create histograms.
Example: If a fair coin is tossed, what is the probability of a head occurring?
P(n) = probability of n occurrencesp= proportion success (what you are looking for)q= proportion failures (what you are not looking for)
6! = 6x5x4x3x2x1=720
z value = distance from the mean measured in standard deviations
So… we first want to stabilize the process, second we will reduce variation and last thing is to center the process.
Remember when we talked about 3? The 3 is the z value.
A positive value indicates a z value to the right of the mean and a negative indicates a z value to the left of the mean.