Empirical Rule

Front

What is the Empirical Rule?

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

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

Back

34%.

Front

In a normal distribution, what percentage of data is less than the mean?

Back

50%.

Front

What percentage of data falls between the mean and two standard deviations above the mean?

Back

47.5%.

Front

If the mean is 70 and the standard deviation is 5, what is the range for one standard deviation above and below the mean?

Back

The range is 65 to 75.

Front

What percentage of data falls between one and two standard deviations above the mean?

Back

13.5%.

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 around the mean.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

95%.

Front

If a dataset is normally distributed with a mean of 12 and a standard deviation of 3, what is the probability of a value being between 12 and 15?

Back

34%.

Front

What is the area under the normal curve for a standard normal distribution?

Back

The total area under the curve is 1 (or 100%).