Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let X be the number of successes in the sample. For which value of p would it be safe to assume the sampling distribution of X is approximately Normal?
A)0.01
B)1/9
C)0.975
D)0.9999

Question

Quizplus · Accepted Answer

The sampling distribution of $X$ can be approximated by a normal distribution if the sample size $n$ and population proportion $p$ satisfy the conditions $np \geq 10$ and $n(1-p) \geq 10$. For $n = 100$, option B) $1/9 \approx 0.111$ satisfies both conditions $100 \times \frac{1}{9} \geq 10$ and $100 \times \frac{8}{9} \geq 10$, making the normal approximation appropriate. Options A, C, and D do not satisfy these conditions as effectively due to very high or very low values of $p$, leading to either $np < 10$ or $n(1-p) < 10$.

Suppose We Select an SRS of Size N = 100