Two standard normal probabilities

Topic: Functions of random variables and limit theorems · more questions on this topic
‹ An affine image of a standard normal Probabilities for a shifted normal ›

Let X be standard normal. Using \Phi(1.3)\approx 0.9032 and \Phi(1.4)\approx 0.9192, evaluate \mathbb{P}(X\le 1.4) and \mathbb{P}(X>-1.3).

Worked answer (click to show)

\mathbb{P}(X\le 1.4)=\Phi(1.4)\approx 0.9192. The standard normal density is symmetric, so \mathbb{P}(X>-1.3)=\mathbb{P}(X<1.3)=\Phi(1.3)\approx 0.9032.