Bernoulli confidence intervals

[Gekko]

Confidence intervals

1. Homework Statement [/

Use CLT to construct approximate symmetric 100(1-alpha)% confidence interval [L,R] for p then show that [L,1] is then an approximate 100(1-alpha/2)% confidence interval for p

The Attempt at a Solution

When [L,1] then we have a one sided confidence interval.
What we effectively need to show is that the area under the normal curve from -inf to alpha/2 is equal to the area under the curve from -inf to alpha/4 + the area under the curve from alpha/4 to inf
I was going to look at the error function as a way to solve this. I haven't managed it though. Any thoughts?

 

[Gekko]

This isn't related to Bernoulli. Thanks to CLT we assume normality so the question is how to formally prove the above in a mathematical way.
Can we just use the CDF?