Z-score, percentile, and empirical rules

Front

What is a Z-score?

Back

Front

How do you calculate a Z-score?

Back

Front

What does a Z-score of -2 indicate?

Back

A Z-score of -2 indicates that the value is 2 standard deviations below the mean.

Front

What is the empirical rule?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Front

If the mean is 300 and the standard deviation is 40, what value corresponds to a Z-score of -2?

Back

Front

What is a percentile?

Back

A percentile is a measure used to indicate the value below which a given percentage of observations in a group of observations falls.

Front

What percentile corresponds to a Z-score of -1.08?

Back

A Z-score of -1.08 corresponds to the 14th percentile.

Front

How do you find the range of values for 68% of data using the empirical rule?

Back

Front

If the mean life of a tire is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of tires?

Back

Front

What is the formula to find the Z-score for a given value?

Back