Normal tail two standard deviations above the mean

Question

A normal random variable $X$ has mean $50$ and variance $4$ . Find $\mathbb{P}(X>54)$ to three decimal places.

Short answer

About $0.023$ . The standard deviation is $2$ , so $54$ sits exactly two standard deviations above the mean and the probability is $1-\Phi(2)\approx 1-0.9772=0.0228$ .

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Lessons behind this question

Continuous Random Variables and Probability Density Functions
The Normal Distribution
Cumulative Distribution Functions

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