Normal Distributions and Z Scores 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. Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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 -2 indicate?

Back

A z-score of -2 indicates that the value is 2 standard deviations below the mean.

Front

What is the empirical rule in statistics?

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.

Front

If a normal distribution has a mean of 100 and a standard deviation of 15, what is the range for approximately 95% of the data?

Back

The range is 70 to 130 (mean ± 2 standard deviations).

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central point of the distribution, where the highest frequency of data points occurs.

Front

How do you interpret a z-score of 1.43?

Back

A z-score of 1.43 indicates that the value is 1.43 standard deviations above the mean.

Front

What is the purpose of using z-scores?

Back

Z-scores allow for comparison of scores from different distributions by standardizing them.