4/8 Normal Distribution Curves

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 does the mean represent in a data set?

Back

The mean represents the average value of a data set, calculated by adding all the numbers and dividing by the count of numbers.

Front

What is the standard deviation?

Back

The standard deviation is a measure of the amount of variation or dispersion in 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

What is the total area under a normal distribution curve?

Back

The total area under a normal distribution curve is equal to 1.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean.

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 is the empirical rule?

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.