Further Applications of Normal Distributions (HSC SSCE Mathematics Standard): Flashcards

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Further Applications of Normal Distributions
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3 equal measures in normal distribution

Mean, mode, and median

Shape of normal distribution around mean

Perfectly symmetrical

Alternative name for 68-95-99.7 rule

Empirical rule

% within 1 SD of mean (zz between −1-1 and 11)

68%

% within 2 SDs of mean (zz between −2-2 and 22)

95%

% within 3 SDs of mean (zz between −3-3 and 33)

99.7%

Formula for z-score

z=x−xˉsz = \frac{x - \bar{x}}{s}

What z-score measures

Standard deviations a value is from mean

% between mean and 1 SD (one side)

34%

% between 1 and 2 SDs (one side)

13.5%

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