Critical Thinking: Brain Teaser A requirement for using the normal distribution to approximate the p distribution is that both np . 5 and nq .

Critical Thinking: Brain Teaser A requirement for using the normal distribution to approximate the pˆ

distribution is that both np . 5 and nq . 5. Since we usually do not know p, we estimate p by pˆ and q by qˆ 512pˆ. Then we require that npˆ . 5 and nqˆ . 5. Show that the conditions npˆ . 5 and nqˆ . 5 are equivalent to the condition that out of n binomial trials, both the number of successes r and the number of failures n 2r must exceed 5. Hint: In the inequality npˆ . 5, replace pˆ by r /n and solve for r. In the inequality nqˆ . 5, replace qˆ by (n 2r)/n and solve for n 2r .

AppendixLO1