z-Scores & Normal Distribution

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What is a z-score?

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A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation.

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How do you calculate a z-score?

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The formula for calculating a z-score is: 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 negative z-score indicate?

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A negative z-score indicates that the value is below the mean of the data set.

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What does a positive z-score indicate?

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A positive z-score indicates that the value is above the mean of the data set.

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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 located at 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 amount of variation or dispersion of a set of values in a normal distribution.

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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: 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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How do you find the probability of a z-score?

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To find the probability of a z-score, you can use a z-table, which provides the area (probability) to the left of a given z-score in a standard normal distribution.

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What is the area under the normal curve?

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The total area under the normal distribution curve is equal to 1, representing the total probability of all outcomes.

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What is the significance of the normal distribution in statistics?

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The normal distribution is significant because many statistical tests and methods assume that the data follows a normal distribution, making it easier to analyze and interpret.