Normal Distributions: Empirical Rule Practice

Front

What is the Empirical Rule in statistics?

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 two standard deviations of the mean in a normal distribution?

Back

95%

Front

What is the shape of a normal distribution curve?

Back

Bell curve

Front

If a dataset is normally distributed with a mean of 50 and a standard deviation of 10, what percentage of data falls between 40 and 60?

Back

68%

Front

What is the z-score formula?

Back

z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

In a normal distribution, what does a z-score of 0 represent?

Back

A z-score of 0 represents a value that is exactly equal to the mean.

Front

What is the significance of the standard deviation in a normal distribution?

Back

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

Front

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

Back

70 to 130.

Front

What is the probability of a value being more than two standard deviations above the mean in a normal distribution?

Back

Approximately 2.5%.

Front

How do you find the area under the normal curve to the left of a given z-score?

Back

Use a z-table or standard normal distribution calculator.