The central limit theorem states that, if a random sample of size $n$ is drawn from a population, then the sampling distribution of the sample mean $\bar{X}$:
A. is approximately normal if the underlying population is normal
B. has the same variance as the population
C. is approximately normal if $n > 30$
D. is approximately normal if $n < 30$

Given that $X$ is a binomial random variable, the binomial probability $P(X=x)$ is approximated by the area under a normal curve between
A. $x-0.5$ and $x+0.5$
B. $1-x$ and $1+x$
C. $x-0.5$ and $0.0$
D. $0.0$ and $x+0.5$