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 one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

If the mean score of a test is 50 and the standard deviation is 10, what is the range for one standard deviation from the mean?

Back

40 to 60.

Front

How do you calculate the z-score?

Back

Z-score = (X - mean) / standard deviation.

Front

What does a z-score represent?

Back

A z-score indicates how many standard deviations an element is from the mean.

Front

In a normal distribution, what does it mean if a z-score is greater than 2?

Back

It means the value is more than 2 standard deviations above the mean, which is rare.

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability, which equals 1.

Front

If a dataset has a mean of 100 and a standard deviation of 15, what is the probability of a value being less than 85?

Back

Approximately 16%.