# 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

Derive $100\left(1-\alpha \right)$ percent lower and upper confidence intervals for p, when the data consist of the values of n independent Bernoulli random variables with parameter p.

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Nicole Conner
Lower confidence interval: $\left(-\mathrm{\infty },\stackrel{⏞}{p}+{z}_{\alpha }\sqrt{\stackrel{⏞}{p}\left(\frac{1-\stackrel{⏞}{p}}{n}\right)}$
Upper confidence interval: $\left(\stackrel{⏞}{p}-{z}_{\alpha }\sqrt{\stackrel{⏞}{p}\left(\frac{1-\stackrel{⏞}{p}}{n}\right),\mathrm{\infty }}\right\}$