Get the solution to "If X is a normal random variable with..."

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varaderiyw

Answered question

2021-11-06

If X is a normal random variable with parameters
$μ = 10$
and
$σ^{2} = 36$
, compute P[4 < X < 16]

Answer & Explanation

Tamara Donohue

Beginner2021-11-07Added 11 answers

Given that X is a mean-containing normal random variable $μ = 10$ and variance $σ^{2} = 36$ .
The following probability will be calculated using the knowledge that if $X \sim N (μ, σ^{2})$ , then $Z = \frac{X - μ}{σ} \sim N (0, 1)$ , i.e; Z is a standard normal variable with $Φ$ being its cdf, whose probabilities are calculable using the normal table.
$P [4 < X < 16] = P [\frac{4 - 10}{6} < \frac{X - μ}{σ} < \frac{16 - 10}{6}]$
=P[-1<Z<1]
$= Φ (1) - Φ (- 1)$
=0.8413-0.1586
=0.6827

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