Standardisation and the 68–95–99.7% Rule (VCE SSCE Mathematical Methods): Quizzes

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Standardisation and the 68–95–99.7% Rule
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What % of values lie within 1 standard deviation of the mean in a normal distribution?

68%

What % of values lie within 2 standard deviations of the mean in a normal distribution?

95%

What % of values lie within 3 standard deviations of the mean in a normal distribution?

99.7%

For IQ scores with μ=100\mu = 100 and σ=15\sigma = 15, what range contains 68% of scores?

85 to 115

For IQ scores with μ=100\mu = 100 and σ=15\sigma = 15, what range contains 95% of scores?

70 to 130

If 95% of values lie within 2 SD of the mean, what % lie outside this region?

5%

If 95% lie within 2 SD, what % are above 2 SD from the mean, using symmetry?

2.5%

What does a negative zz-value indicate about a data value?

It lies below the mean

For IQ with μ=100\mu = 100, σ=15\sigma = 15, calculate zz for a score of 90.

z0.67z \approx -0.67

What are the mean and standard deviation of the standard normal distribution?

μ=0\mu = 0, σ=1\sigma = 1

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