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

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Further Applications of Normal Distributions
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In a normal distribution, which measures are equal?

Mean, mode, and median

What percentage of values fall within 1 SD of the mean?

68%

What percentage of values have z-scores between −2-2 and 22?

95%

What percentage of values fall within 3 SD of the mean?

99.7%

What is the formula for calculating a z-score?

z=x−xˉsz = \frac{x - \bar{x}}{s}

If mean is 150150 and SD is 55, what is the z-score for 145145?

−1-1

What percentage of values fall below the mean?

50%

What percentage falls between the mean and 1 SD above?

34%

What percentage of values have z-scores above 22?

2.5%

If mean is 420420 and SD is 33, what % are below 423423?

84%

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