Normal Distributions: Empirical Rule Practice

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 is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Front

What percentage of data falls outside three standard deviations of the mean in a normal distribution?

Back

Approximately 0.3%.

Front

If the mean of a normal distribution is 50 and the standard deviation is 2, what is the range for one standard deviation from the mean?

Back

The range is from 48 to 52.

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 in a normal distribution?

Back

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

Front

In a normal distribution, what does it mean if a z-score is positive?

Back

A positive z-score indicates that the data point is above the mean.

Front

In a normal distribution, what does it mean if a z-score is negative?

Back

A negative z-score indicates that the data point is below the mean.