Answer to Question #128202 in Statistics and Probability for Abby

Question

What is the smallest sample size needed so that a sampling distribution of a sample proportion can be claimed approximately normal from a population with a proportion of p=15%?

(Round to the next whole number)

Answer 1

The proportion of a random sample has a sampling distribution whose shape can be approximated by a normal model if $np\geq10$ and $np(1-p)\geq10.$

Given $p=0.15$

$$0.15n\geq10$$ $$0.15(1-0.15)n\geq10$$

$$n\geq\dfrac{10}{0.15}$$ $$n\geq\dfrac{10}{0.15\cdot0.85}$$

Since $n$ is integer

$$n\geq79$$

The smallest sample size is $79.$