Question

No replacement To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size $n$be no more than $10\%$of the population size$N$?

Short answer

The probability of success will change, particularly after each drawn element.

Step-by-step solution

Given information

The sample size $n$be no more than $10\%$of the population size $N$in a binomial distribution.

Explanation

The Sample Size $\left(n\right)>10\%$of population $\left(\mathrm{N}\right)$

And the probability of success $\left(P\right)$will alter with each draw; replacement will not be used. As a result, the binomial distribution formula cannot be utilized in this case.

If the sample size is more than $10\%$, the probability of success will fluctuate after each draw.