Normal Distributions and Z-scores

Front

What is standard deviation?

Back

The average distance that data points are from the average.

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 all tires?

Back

28,000 km and 32,000 km.

Front

What is the z-score of a teenage male with a waist size of 33 inches if the average waist size is 29 inches with a standard deviation of 2 inches?

Back

2

Front

What does a Z-score of -1.5 indicate?

Back

The score is 1.5 standard deviations below the average.

Front

If I have a positive z-score, did I score above or below the mean?

Back

ABOVE

Front

What is a normal distribution?

Back

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

What is the formula for calculating a z-score?

Back

Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score of 0 represent?

Back

The score is exactly at the mean.

Front

What is the empirical rule in statistics?

Back

In a normal distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations from the mean.