Normal Distribution Practice (FinAlg)

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What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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What are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of data falls within one standard deviation of the mean.

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

Back

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

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How do you calculate a z-score?

Back

Z-score = (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 indicates how many 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?

Back

The area under the normal curve represents the probability of a value falling within a certain range. The total area is equal to 1.

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How do you find the percentile rank of a score?

Back

Percentile rank is found by determining the percentage of scores that fall below a given score in a distribution.

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What is the relationship between z-scores and percentiles?

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Z-scores can be used to find percentiles in a normal distribution by determining the area to the left of the z-score.

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What is the standard normal distribution?

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The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

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How do you interpret a z-score of -3?

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A z-score of -3 indicates that the value is 3 standard deviations below the mean, which is very rare in a normal distribution.