Tag Archives: Geometric Probability Model

AP Statistics Assignment for 1/29

From chapter 16, read pages 418-423, up to the section titled “The Normal Model to the Rescue!”

From the exercises on pages 430-432, do 7, 10, 12, 17

A word about assumptions and conditions…

In order for a model (e.g., a normal model or binomial probability model) to be valid for a scenario, we must be able to make certain assumptions about that scenario.  These assumptions can include the results of individual trials being independent from each other, the distribution of results being sufficiently unimodal and symmetric, etc.

If it is appropriate to make these assumptions, then go ahead and do it. But if it is not appropriate to make these assumptions, you can still proceed provided certain conditions are satisfied.  These conditions mean that the scenario is “close enough” to allow the model to be valid.

For example, coin flips are independent.  There is no finite population of coin flips that you are “drawing” a sample from, and so each coin flip’s outcome is independent of the next.  Drawing cards from a deck are not independent, as the deck is finite and the probability of a certain outcome changes with each card that is removed. However, if the population is large enough, or more specifically if the sample is small enough in comparison to the population, then that probability change is very small, small enough to be ignored.

In general, as long as the sample size is less than 10% of the overall population, the probability change isn’t big enough to be worrisome. The reason why the magic number is 10% has to do with something called the Finite Population Correction Factor, and a thorough description of where it comes from and how it affects probabilities can be found here.