In order to justify using any mathematical model, we make a series of assumptions. Assumptions are assumed, and therefore are difficult, if not impossible, to check. Therefore, each assumption has a related condition to check in order to determine if it reasonable to make the relevant assumption. These conditions still don't guarantee that we have met the assumptions, but they make us feel more confident that they are ok assumptions to make.

The assumptions and conditions to justify using the normal model when modeling the distribution of sample proportions are listed in the table below. Read them closely.

$\backslash$table$[[$Modeling Sampling Distributions of Sample Proportions$],[,$Assumption is true...,...if this condition is met$],[$Assumption $1,\backslash$table$[[$The sampled values are$],[$independent of each other$]],\backslash$table$[[10\%$ Condition: if sampling has not been$],[$made with replacement $($this is$,$ returning$],[$each sampled individual to the population$],[$before drawing the next individual$),$ then$],[$sample size, $n,$ must be no larger than $10\%$ of$],[$the population$]]],[$Assumption $2,\backslash$table$[[$The sample size, $n,$ is large$],[$enough$]],\backslash$table$[[$Success$/$failure Condition: the sample size$],[$must be large enough so that: $np>10$ and$],[nq>10$