Given a binomial distribution with $n$ trials and probability $p$ of success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if
A. $np \geq 5$ and $n(1-p) \leq 5$
B. $np \leq 5$ and $n(1-p) \geq 5$
C. $np \geq 5$ and $n(1-p) \geq 5$
D. $np \leq 5$ and $n(1-p) \leq 5$

If two populations are normally distributed, the sampling distribution of the sample mean difference $\bar{X_1}-\bar{X_2}$ will be:
A. normally distributed
B. normally distributed only if both population sizes are greater than 30
C. approximately normally distributed
D. normally distributed only if both sample sizes are greater than 30