Front

What is the mean (μ) in a normal distribution?

Back

The mean (μ) is the average value of a set of data points in a normal distribution, representing the center of the distribution.

Front

What is the standard deviation (σ) in a normal distribution?

Back

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

Front

What does it mean if a distribution is normal?

Back

A normal distribution is a symmetric, bell-shaped distribution where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

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What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data falls within one standard deviation (μ ± σ) of the mean.

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What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations (μ ± 2σ) of the mean.

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What percentage of data falls within three standard deviations of the mean in a normal distribution?

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Approximately 99.7% of the data falls within three standard deviations (μ ± 3σ) of the mean.

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How do you find the z-score for a given value in a normal distribution?

Back

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 is the significance of the z-score in a normal distribution?

Back

The z-score indicates how many standard deviations a value is from the mean, helping to determine the probability of a value occurring.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.

Front

How do you calculate the probability of a value falling below a certain z-score?

Back

You can use the standard normal distribution table (z-table) to find the probability corresponding to a given z-score.