Normal Distribution

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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, where the mean, median, and mode are all equal. It is defined by its mean (μ) and standard deviation (σ).

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

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

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What does the mean represent in a normal distribution?

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The mean (μ) represents the average value of the data set and is the center of the normal distribution curve.

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What does the standard deviation represent in a normal distribution?

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The standard deviation (σ) measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean.

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

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

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The z-score indicates how many standard deviations a value (X) is from the mean. A positive z-score means the value is above the mean, while a negative z-score means it is below the mean.

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How do you find the probability of a range of values in a normal distribution?

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To find the probability of a range of values, calculate the z-scores for both values, then use the standard normal distribution table (z-table) to find the probabilities corresponding to those z-scores and subtract them.

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What is the area under the normal distribution curve?

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

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What is the middle 30% of a normal distribution?

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The middle 30% of a normal distribution refers to the range of values that fall between the 35th percentile and the 65th percentile.

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How do you determine the lightest 22% of cans in a normal distribution?

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