Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

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Critical Thinking: Brain Teaser A requirement for using the normal distribution to approximate the
distribution is that both np 5 and nq 5. Since we usually do not known 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 trails, both the number of successes r and the number of failures n - r must exceed 5. Hint: 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.