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Formula

Normal probability distribution

X ~ N ( μ , σ )

μ = the mean σ = the standard deviation

Formula

Standard normal probability distribution

Z ~ N ( 0 , 1 )

z = a standardized value (z-score)

mean = 0 standard deviation = 1

Formula

Finding the kth percentile

To find the kth percentile when the z-score is known: k = μ + ( z ) σ

Formula

Z-score

z = x - μ σ

Formula

Finding the area to the left

The area to the left: P ( X x )

Formula

Finding the area to the right

The area to the right: P ( X x ) = 1 - P ( X x )

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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