Normal Distribution Flashcard - AP Stats

Front

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.

Front

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.

Front

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.

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 does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

Front

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 under the curve equals 1, representing 100% probability.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution and is located at the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation 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.

Front

How do you find the percentile rank of a value in a normal distribution?

Back

To find the percentile rank, calculate the z-score for the value, then use the z-table to find the corresponding percentile.

Front

What is the purpose of a z-table?

Back

A z-table provides the area (probability) to the left of a given z-score in a standard normal distribution, helping to determine percentiles.