Area under Normal Distribution (Leaving Cert Mathematics): Flashcards

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Area under Normal Distribution
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Area under normal distribution curve represents

Probabilities

Shape of normal distribution

Bell-shaped, symmetric about the mean

Mean (μ\mu) of standard normal distribution

0

Std deviation (σ\sigma) of standard normal distribution

1

Z-score formula

Z=X−μσZ = \frac{X - \mu}{\sigma}

Z-score indicates

How many standard deviations a value is from the mean

XX in Z-score formula represents

The value in the dataset

μ\mu in Z-score formula represents

The mean of the dataset

σ\sigma in Z-score formula represents

The standard deviation of the dataset

Z-table provides

Cumulative area (probability) to left of a given Z-score

Finding probability between two Z-values

Subtract smaller Z-area from larger Z-area

Total area under normal distribution curve

1 (representing 100% probability)

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Empirical Rule

Standard Deviation

Normal Distributions/Z-Scores

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Empirical Rule

Standard Deviation

Normal Distributions/Z-Scores

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Empirical Rule

Standard Deviation

Normal Distributions/Z-Scores

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Empirical Rule

Standard Deviation

Normal Distributions/Z-Scores

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