Empirical Rule and Normal Distributions Flashcard

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

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (x - mean) / standard deviation, where x is the value for which you are calculating the z-score.

Front

What percentage of data lies below the mean in a normal distribution?

Back

In a normal distribution, 50% of the data lies below the mean.

Front

If a normal distribution has a mean of 100 and a standard deviation of 15, what is the z-score for a value of 130?

Back

The z-score is calculated as z = (130 - 100) / 15 = 2.

Front

What does a z-score of 0 indicate?

Back

A z-score of 0 indicates that the value is exactly equal to the mean of the distribution.

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean; a smaller standard deviation indicates that the data points are closer to the mean.

Front

In a normal distribution, what percentage of data falls within two standard deviations of the mean?

Back

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Front

How do you interpret a negative z-score?

Back

A negative z-score indicates that the value is below the mean of the distribution.

Front

What is the relationship between the mean and median in a normal distribution?

Back

In a normal distribution, the mean and median are equal.

Front

If a test score is 85, the mean is 75, and the standard deviation is 5, what is the z-score?

Back

The z-score is calculated as z = (85 - 75) / 5 = 2.