68-95-99.7 Rule (Empirical Rule)

Front

What is the 68-95-99.7 Rule?

Back

The 68-95-99.7 Rule, also known as the Empirical Rule, states that for a normal distribution: 68% of data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

68% of the data falls within one standard deviation of the mean.

Front

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

Back

95% of the data falls within two standard deviations of the mean.

Front

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

Back

99.7% of the data falls within three standard deviations of the mean.

Front

If a GPA is normally distributed with a mean of 2.9 and a standard deviation of 0.6, what percentage of students have a GPA between 2.3 and 3.5?

Back

68% of students have a GPA between 2.3 and 3.5.

Front

In a normal distribution, what does it mean if data is one standard deviation above the mean?

Back

It means that the data point is greater than the mean by the amount of the standard deviation, indicating it is higher than approximately 68% of the data.

Front

For a machine producing components with lengths normally distributed, if 99.7% of components are between 1.176 cm and 1.224 cm, what are the mean and standard deviation?

Back

Mean = 1.200 cm, Standard Deviation = 0.008 cm.

Front

What is the interval that contains approximately 95% of the weights filled by a machine with a mean of 1150 pounds and a standard deviation of 22 pounds?

Back

The interval is 1106 to 1194 pounds.

Front

What does it mean if a data point is more than two standard deviations above the mean in a normal distribution?

Back

It indicates that the data point is higher than approximately 97.5% of the data.

Front

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

Back

The range is calculated as: Mean ± 2(Standard Deviation).