68-95-99.7 Rule (Empirical Rule)

Front

What is the 68-95-99.7 Rule (Empirical Rule)?

Back

The 68-95-99.7 Rule states that for a normal distribution, approximately 68% of the 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

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 a normal distribution has a mean of 100 and a standard deviation of 10, what is the interval that contains approximately 95% of the data?

Back

The interval is from 80 to 120.

Front

In a normal distribution, how do you calculate the interval for 95% of the data?

Back

You take the mean and subtract/add two times the standard deviation.

Front

What is the z-score for a value that is one standard deviation above the mean?

Back

The z-score is +1.

Front

What is the z-score for a value that is two standard deviations below the mean?

Back

The z-score is -2.

Front

How do you find the probability of a value being less than a certain number in a normal distribution?

Back

You can use the z-score formula and refer to the standard normal distribution table.

Front

If a normal distribution has a mean of 50 and a standard deviation of 5, what is the probability of a value being less than 40?

Back

Approximately 2.5%.