AP Statistics 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.

Front

What does the mean represent in a normal distribution?

Back

The mean represents the average value of the data set and is the center of the normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

How do you calculate the z-score?

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.

Front

What is the significance of the z-score?

Back

The z-score indicates how many standard deviations a data point is from the mean, helping to understand its position within the distribution.

Front

What area under the normal curve corresponds to a z-score of 1?

Back

Approximately 84% of the data falls below a z-score of 1, meaning the area to the left of z = 1 is 0.8413.

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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 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

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How do you find the area to the right of a z-score?

Back

To find the area to the right of a z-score, subtract the area to the left from 1 (e.g., Area to the right = 1 - Area to the left).

Front

What is the probability of a value falling within a certain range in a normal distribution?

Back

The probability can be found by calculating the area under the curve between the two z-scores corresponding to the values.

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How do you determine the cutoff for the top 10% in a normal distribution?

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To find the cutoff for the top 10%, locate the z-score that corresponds to the 90th percentile and then use the mean and standard deviation to find the value.