I have the following standard normal CDF $$\max \Phi(2\times\sqrt{n}(c_1-0.48)) = 0.025$$ $$\max P(Z<2\times\sqrt{n}(c_1-0.48)) = 0.025$$
I am trying to get the value for $c_1$.
Is it correct to set $Z = 1.96$ (since 0.025 quantile) and then set $$1.96 = 2\times\sqrt{n}(c_1-0.48)$$
Solving for $c_1 = \frac{1.96}{2\sqrt{n}}+0.48$
Seems I am going wrong somewhere..