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 within 1 standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

If the mean weight of concrete is 1150 pounds and the standard deviation is 22 pounds, what is the weight range for approximately 95% of molds?

Back

The weight range is approximately 1106 to 1194 pounds.

Front

What is the weight range for approximately 68% of molds if the mean is 1150 pounds and the standard deviation is 22 pounds?

Back

The weight range is approximately 1128 to 1172 pounds.

Front

What is the area under the normal distribution curve between 1 and 2 standard deviations from the mean?

Back

Approximately 13.5%.

Front

What is the area under the normal distribution curve between the mean and 1 standard deviation?

Back

Approximately 34%.

Front

In a normal distribution, what does it mean if a data point is more than 2 standard deviations away from the mean?

Back

It indicates that the data point is in the tail of the distribution and is less common.

Front

How do you calculate the interval for 95% of data in a normal distribution?

Back

Use the formula: Mean ± 2(Standard Deviation). For example, with a mean of 1150 and a standard deviation of 22, the interval is 1150 ± 2(22) = 1106 to 1194.