A greenhouse in a tri-county area has kept track of its customers for the last several years and has determinedthat it has about 10,000 regular customers. Of those customers, 28% of them plant a vegetable garden in thespring. The greenhouse obtains a random sample of 800 of its customers. Is it safe to assume that the sampling^distribution of p, the sample proportion of customers that plant a vegetable garden, is approximately normal?
A) Yes
B) No

Question

Quizplus · Accepted Answer

The sampling distribution of the sample proportion $p$ can be considered approximately normal if the sample size $n$ meets the conditions $np \geq 10$ and $n(1-p) \geq 10$. Given $n = 800$ and $p = 0.28$, $np = 800(0.28) = 224$ and $n(1-p) = 800(0.72) = 576$, both of which are greater than 10, thus satisfying the conditions for normal approximation.

A Greenhouse in a Tri-County Area Has Kept Track of Its