Empirical Rule - Shaded

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 is within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

If 50% of the data is shaded in a normal distribution, what does this represent?

Back

This represents the median of the distribution, where half of the data lies below and half lies above.

Front

In a normal distribution, if 5% of the data is in the tails, what percentage is in the middle?

Back

95% of the data is in the middle.

Front

In a normal distribution, if 2.5% is in each tail, what percentage is in the middle?

Back

95% of the data is in the middle.

Front

What does it mean if 16% of the data is shaded in a normal distribution?

Back

This means that 16% of the data falls between the mean and one standard deviation below the mean.

Front

How do you calculate the percentage of data in a shaded region using the Empirical Rule?

Back

Identify the number of standard deviations from the mean that the shaded region covers and apply the corresponding percentages: 68%, 95%, or 99.7%.

Front

What is the significance of the area under the curve in a normal distribution?

Back

The area under the curve represents the total probability, which equals 1 (or 100%).