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What is a Normal distribution?

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A Normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, defined by its mean (average) and standard deviation (spread).

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What does the mean represent in a Normal distribution?

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The mean represents the central point of the distribution, where the highest frequency of data points occurs.

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What does the standard deviation indicate in a Normal distribution?

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The standard deviation indicates the dispersion or spread of the data points around the mean. A smaller standard deviation means data points are closer to the mean.

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What is a z-score?

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A z-score measures how many standard deviations a data point is from the mean of the distribution. It indicates the relative position of a value within a distribution.

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How do you calculate a z-score?

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The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What does it mean if a distribution is skewed to the right?

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A right-skewed distribution has a longer tail on the right side, indicating that most data points are concentrated on the left with fewer high values.

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What is the empirical rule (68-95-99.7 rule)?

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The empirical rule states that in a Normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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What is the significance of the area under the Normal curve?

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The area under the Normal curve represents the total probability of all outcomes, which equals 1. Specific areas correspond to probabilities of certain ranges of values.

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How do you find the proportion of data above a certain z-score?

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To find the proportion of data above a certain z-score, you can use z-tables or standard Normal distribution calculators to find the area to the left of the z-score and subtract it from 1.

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What is a standardized score?

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A standardized score, or z-score, allows comparison of scores from different distributions by converting them to a common scale with a mean of 0 and a standard deviation of 1.