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 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 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 standard deviations, and 99.7% within three standard deviations of the mean.

Front

What does it mean if a distribution is skewed left?

Back

A left-skewed distribution has a longer tail on the left side, indicating that the majority of the data points are concentrated on the right.

Front

What does it mean if a distribution is skewed right?

Back

A right-skewed distribution has a longer tail on the right side, indicating that the majority of the data points are concentrated on the left.

Front

What is the shape of a normal distribution?

Back

The shape of a normal distribution is bell-shaped and symmetric around the mean.

Front

What is a standard deviation?

Back

A standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

How do you calculate the z-score?

Back

The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation: z = (X - μ) / σ.