Normal Distribution

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 is the Empirical Rule?

Back

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

Front

What does the mean represent in a normal distribution?

Back

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

Front

What does the standard deviation indicate?

Back

The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean.

Front

How do you calculate the percentage of data within one standard deviation of the mean?

Back

According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

Front

How do you calculate the percentage of data within two standard deviations of the mean?

Back

According to the Empirical Rule, approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Front

How do you calculate the percentage of data within three standard deviations of the mean?

Back

According to the Empirical Rule, approximately 99.7% of the data falls within three standard deviations of the mean in a normal distribution.

Front

If the mean is 38 and the standard deviation is 4, what is the range for 68% of the data?

Back

The range for 68% of the data is from 34 to 42 (mean ± 1 standard deviation).

Front

If the mean is 30,000 km and the standard deviation is 2,000 km, what is the range for 68% of the tire life?

Back

The range for 68% of the tire life is from 28,000 km to 32,000 km (mean ± 1 standard deviation).

Front

What is the z-score formula?

Back

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