Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$, and $X$ is the number of successes in the sample.
$$n = 77 , p = 0.33 : P ( X \leq 18 )$$
A) 0.0418
B) 0.0475
C) 0.9525
D) 0.0582

Question

Quizplus · Accepted Answer

The normal approximation to the binomial distribution can be used here. First, calculate the mean $\mu = np = 77 \times 0.33 = 25.41$ and the standard deviation $\sigma = \sqrt{np(1-p)} = \sqrt{77 \times 0.33 \times 0.67} \approx 4.22$. Then, use the continuity correction factor to find $P(X \leq 18.5)$. Convert to a z-score: $z = \frac{18.5 - 25.41}{4.22} \approx -1.64$. Using the standard normal distribution table, $P(Z \leq -1.64) \approx 0.0475$.

Use the Normal Approximation to Find the Indicated Probability ppp , And

Use the Normal Approximation to Find the Indicated Probability $p$ , And