Assume that $x$ is a binomial random variable with $\mathrm { n } = 400$ and $\mathrm { p } = 0.30$. Use a normal approximation to find $P ( x \geq 100 )$.
A) 0.9875
B) 0.5948
C) 0.9834
D) 0.4875

Question

Quizplus · Accepted Answer

The correct answer is A.The mean of the binomial distribution is $\mu = np = 400 \times 0.30 = 120$. The standard deviation is $\sigma = \sqrt{np(1-p)} = \sqrt{400 \times 0.30 \times 0.70} = 10.95$.Using the normal approximation to the binomial distribution, we have:$$P(X \geq 100) \approx P(Z \geq \frac{100 - 120}{10.95}) = P(Z \geq -1.82) = 0.9875$$where Z is a standard normal random variable.

Assume That xxx Is a Binomial Random Variable With n=400\mathrm { n } = 400n=400

Assume That $x$ Is a Binomial Random Variable With $\mathrm { n } = 400$