Question

Why is it necessary to check that n modifyingabove p with caret greater than or equals 5np≥5 and n modifyingabove q with caret greater than or equals 5nq≥5​?

Answer 1

Both of these conditions must be true in order for the assumption that the binomial distribution is approximately normal. In other words, if $np \ge 5$ and $nq \ge 5$ then we can use a normal distribution to get a good estimate of the binomial distribution. If either np or nq is smaller than 5, then a normal distribution wouldn't be a good model to use.

side note: q = 1-p is the complement of probability p