To use the large sample confidence interval for p, you need at least 15 successes and 15

Question:

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 p̂ = 0.50.
b) 50 when p̂ = 0.30.
(c) 150 when p̂ = 0.10. That is, the overall n must increase as p̂ moves toward 0 or 1. (When the true proportion is near 0 or 1, the sampling can be highly skewed unless n is quite large.)
Distribution
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