Empirical Rule Practice

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

68%.

Front

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

Back

95%.

Front

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

Back

99.7%.

Front

If the mean age of golfers is 38 and the standard deviation is 4, what is the age range for the middle 68% of golfers?

Back

The age range is from 34 to 42 years old (38 ± 4).

Front

If the mean is 50 and the standard deviation is 10, what is the range for the middle 95% of the data?

Back

The range is from 30 to 70 (50 ± 20).

Front

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

Back

It is considered an outlier.

Front

In a normal distribution, what percentage of data is below the mean?

Back

50%.

Front

If a data set is normally distributed with a mean of 100 and a standard deviation of 15, what is the z-score for a value of 130?

Back

The z-score is 2 (130 - 100) / 15.

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 (or 100%).