A requirement for using the normal distribution to approximate the  distribution is that both np > 5 and nq > 5. Since we usually do not know p, we estimate p by  and q by  = 1 - . Then we require that n > 5 and n > 5. Show that the conditions n > 5 and n > 5 are equivalent to the condition that out of n binomial trials, both the number of successes r and the number of failures n - r exceed 5. In the inequality n > 5, replace  by r/n and solve for r. In the inequality n > 5, replace  by (n – r)/n and solve for n - r.