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 shape does a normal distribution curve have?

Back

A normal distribution curve has a bell shape.

Front

What is the mean in a normal distribution?

Back

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

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion of a set of values.

Front

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

Back

Approximately 68% of the data falls within one standard deviation of the mean.

Front

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

Back

Approximately 95% of the data falls within two standard deviations of the mean.

Front

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

Back

Approximately 99.7% of the data falls within three standard deviations of the mean.

Front

If the mean is 6.4 and the standard deviation is 1.5, what is the z-score for 7 accidents?

Back

The z-score is calculated as (X - mean) / standard deviation = (7 - 6.4) / 1.5 = 0.4.

Front

How do you find the proportion of data above a certain value in a normal distribution?

Back

You can use the z-score to find the proportion of data above a certain value using standard normal distribution tables.

Front

What is the empirical rule in statistics?

Back

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