Normal Distribution Lessons 3-4

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 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 is standard deviation in the context of normal distribution?

Back

Standard deviation measures the amount of variation or dispersion of a set of values. In a normal distribution, it determines the width of the bell 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 tell you?

Back

A z-score indicates how many standard deviations an element is from the mean. A positive z-score means the value is above the mean, while a negative z-score means it is below the mean.

Front

What percent 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 in a normal distribution.

Front

What percent 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 in a normal distribution.

Front

What percent 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 in a normal distribution.

Front

If the mean number of accidents is 6.4 and the standard deviation is 1.5, what is the z-score for 5 accidents?

Back

The z-score for 5 accidents is -0.93.

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 from the mean.