8.109 Need 15 successes and 15 failures To use the large-sample confidence interval for p, you need at least 15 successes and 15 failures. Show that the smallest value of n for which the method can be used is

(a) 30 when pn = 0.50,

(b) 50 when pn = 0.30,

(c) 150 when pn = 0.10. That is, the overall n must increase as pn moves toward 0 or 1. (When the true proportion is near 0 or 1, the sampling distribution can be highly skewed unless n is quite large.)