A normal distribution has mean μ and standard deviation σ . An x-value is randomly selected from the distribution. Find P(x≤μ+2σ)

Question

A normal distribution has mean μ and standard deviation σ. An x-value is randomly selected from the distribution. Find P(x≤μ+2σ)

Answer 1

P(x <= µ + 2 σ) = P(z <= 2), where z ~ N(0, 1) (referred to as the standard normal distribution)

Th standard normal distribution is what we find on calculators, in statistics tables, etc.

In Excel, you use normsdist(2) = 0.9772