Normal distribution: PDF and key properties.

easy

Answer

$N({\mu}, \;{\sigma}^{2})$
$Bell-shaped, symmetric around μ. ~68% of mass within 1σ, ~95% within 2σ, ~99.7% within 3σ.$
$Sum of independent normals is normal.$
$Standardized: Z = (X-μ)/σ ~ N(0,1).$
$Universally used because of CLT — many sample statistics are approximately normal for large n.$

Check yourself — multiple choice

Uniform-shaped
Bell curve; 68/95/99.7 rule; sum of independent normals is normal; universal due to CLT
Discrete only
Non-symmetric

Normal: bell curve with 68/95/99.7 rule + closed under sums.

#distributions#probability

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