Normal Distribution

Front

What is a Normal Distribution?

Back

A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

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What are the key properties of a Normal Distribution?

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1. Symmetrical about the mean. 2. Mean = Median = Mode. 3. Approximately 68% of data falls within one standard deviation of the mean. 4. Approximately 95% falls within two standard deviations.

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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: - About 68% of data falls within 1 standard deviation of the mean. - About 95% falls within 2 standard deviations. - About 99.7% falls within 3 standard deviations.

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How do you calculate the 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 a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

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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 probabilities. The total area under the curve is equal to 1, indicating that the total probability of all outcomes is 100%.

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What is the mean in a normal distribution?

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The mean is the average of all data points in a normal distribution and is the center of the distribution.

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What is the standard deviation in a normal distribution?

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The standard deviation measures the dispersion or spread of data points around the mean in a normal distribution.

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How do you find the percent of people scoring above a certain value in a normal distribution?

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To find the percent of people scoring above a certain value, calculate the z-score for that value, then use the z-table to find the area to the left of that z-score and subtract it from 1.

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What is the normal range (68%) for a given mean and standard deviation?

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The normal range (68%) can be found by calculating: (mean - standard deviation, mean + standard deviation).