Normal Distribution Practice

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 mean in a normal distribution?

Back

The mean is the average of all data points in a distribution, and in a normal distribution, it is also the peak of the curve.

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. In a normal distribution, it determines the width of the curve.

Front

How do you calculate the z-score?

Back

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

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

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, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

What is the significance of a z-score of 0?

Back

A z-score of 0 indicates that the data point is exactly at the mean of the distribution.

Front

How do you interpret a z-score of 2.5?

Back

A z-score of 2.5 indicates that the data point is 2.5 standard deviations above the mean.

Front

What percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34% of the data falls between the mean and one standard deviation above the mean.

Front

What is the area under the normal distribution curve?

Back

The total area under the normal distribution curve is equal to 1, representing the total probability of all outcomes.