Question

# Derive 100(1−α) percent lower and upper confidence intervals for p, when the data consist of the values of n independent Bernoulli random variables wi

Upper level probability
Derive $$100(1-\alpha)$$ percent lower and upper confidence intervals for p, when the data consist of the values of n independent Bernoulli random variables with parameter p.
Lower confidence interval: $$\displaystyle{\left(-\infty,\overbrace{{{p}}}+{z}_{{\alpha}}\sqrt{{\overbrace{{{p}}}{\left({\frac{{{1}-\overbrace{{{p}}}}}{{{n}}}}\right)}}}\right.}$$
Upper confidence interval: $$\displaystyle{\left(\overbrace{{{p}}}-{z}_{{\alpha}}\sqrt{{\overbrace{{{p}}}{\left({\frac{{{1}-\overbrace{{{p}}}}}{{{n}}}}\right)},\infty}}\right\rbrace}$$