Normal Distribution Flashcard Review

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 does the mean represent in a normal distribution?

Back

The mean is the average value of the dataset and is the center point 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

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean.

Front

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.

Front

What does a z-score of 1.5 mean?

Back

A z-score of 1.5 means the value is 1.5 standard deviations above the mean.

Front

What is the 12th percentile in a normal distribution?

Back

The 12th percentile is the value below which 12% of the data falls.

Front

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

Back

Use the z-score to find the corresponding percentile from the standard normal distribution table.

Front

What does it mean if a value has a z-score greater than 3?

Back

It indicates that the value is unusually high or low compared to the mean, as it is more than 3 standard deviations away.