Inferential Statistics (Leaving Cert Mathematics): Quizzes

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The Normal Distribution and the Empirical Rule
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What shape does a normal distribution form when data is arranged in a frequency distribution?

Bell-shaped and symmetrical

What does standard deviation (σ\sigma) measure in a normal distribution?

How spread out data is from the mean

According to the empirical rule, what percentage of values lie within one standard deviation?

68%

What percentage of values lie within two standard deviations of the mean?

95%

What percentage of values lie within three standard deviations of the mean?

99.7%

If xˉ=80\bar{x} = 80 and σ=10\sigma = 10, what is xˉσ\bar{x} - \sigma?

70

If xˉ=45\bar{x} = 45 and σ=5\sigma = 5, what range contains 68% of the distribution?

[40, 50]

If xˉ=100\bar{x} = 100 and σ=8\sigma = 8, what range contains 95% of the distribution?

[84, 116]

If mean is 60 and 95% of values are between 48 and 72, what is σ\sigma?

6

If 68% of values fall within a certain range, what is this expressed as a probability?

0.68

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