A normal approximation in the tail

Topic: Functions of random variables and limit theorems · more questions on this topic
‹ The mean of repeated voltage readings A quadratic function of a uniform variable ›

Let X\sim\operatorname{Bin}(100,1/2). Approximate \mathbb{P}(X\ge 60) by a normal probability. Use \Phi(2)\approx 0.97725.

Worked answer (click to show)

The approximating normal has mean 50 and variance 25.

\mathbb{P}(Y\ge 60)=\mathbb{P}\bigl(Z\ge (60-50)/5\bigr)=\mathbb{P}(Z\ge 2)=1-\Phi(2)\approx 0.0228.