Assume that $x$ is a binomial random variable with $\mathrm { n } = 1000$ and $\mathrm { p } = 0.80$. Use a normal approximation to find $\mathrm { P } ( 800

Question

Assume that $x$ is a binomial random variable with $\mathrm { n } = 1000$ and $\mathrm { p } = 0.80$. Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 825 )$.
A) 0.4578
B) 0.0636
C) 0.4623
D) 0.4783

Quizplus · Accepted Answer

Using the normal approximation, $x$ is approximately $N(np, np(1-p))$. Here, $\mu = 800$ and $\sigma = \sqrt{160} \approx 12.65$. Applying continuity correction, calculate $P(800.5 < x \leq 825.5)$ using the standard normal distribution.

Assume That xxx Is a Binomial Random Variable With n=1000\mathrm { n } = 1000n=1000

Assume That $x$ Is a Binomial Random Variable With $\mathrm { n } = 1000$