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Summary of Formulas

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Formula 1: Normal Probability Distribution

X X~ N ( μ , σ ) N(μ,σ)

μμ = the mean σσ = the standard deviation

Formula 2: Standard Normal Probability Distribution

Z Z~ N ( 0 , 1 ) N(0,1)

zz = a standardized value (z-score)

mean = 0 standard deviation = 1

Formula 3: Finding the kth Percentile

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

Formula 4: z-score

z = x - μ σ z= x - μ σ

Formula 5: Finding the area to the left

The area to the left: P ( X < x ) P ( X x )

Formula 6: Finding the area to the right

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

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