Normal Distributions (Empirical Rule)

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution: about 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 lies within ±1 standard deviation in a normal distribution?

Back

68% of the data.

Front

What percentage of data lies within ±2 standard deviations in a normal distribution?

Back

95% of the data.

Front

What percentage of data lies outside of ±3 standard deviations in a normal distribution?

Back

0.3% of the data.

Front

If the mean is 15 and the standard deviation is 3, what is the interval that contains 95% of the data?

Back

9 to 21.

Front

How do you calculate the interval for ±1 standard deviation from the mean?

Back

Mean ± 1(Standard Deviation). For a mean of 15 and standard deviation of 3, the interval is 12 to 18.

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central value around which the data is distributed, and it is also the peak of the normal distribution curve.

Front

What does it mean if a data point is more than 3 standard deviations away from the mean?

Back

It is considered an outlier, as it falls outside the range where 99.7% of the data lies.

Front

In a normal distribution, what does the area under the curve represent?

Back

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