Assume that $x$ is a binomial random variable with $\mathrm { n } = 100$ and $\mathrm { p } = 0.60$. Use a normal approximation to find $P ( x \leq 55 )$.
A) 0.3212
B) 0.1788
C) 0.4247
D) 0.1314

Question

Quizplus · Accepted Answer

To use the normal approximation, calculate the mean $\mu = np = 60$ and standard deviation $\sigma = \sqrt{np(1-p)} = 4.899$. Convert $x = 55$ to a z-score: $z = \frac{55 - 60}{4.899} \approx -1.02$. Using the standard normal distribution table, $P(z \leq -1.02) \approx 0.1788$.

Assume That xxx Is a Binomial Random Variable With n=100\mathrm { n } = 100n=100

Assume That $x$ Is a Binomial Random Variable With $\mathrm { n } = 100$