Prob/Stats - Lesson 4.2 Activity - Empirical Rule/Normal

Front

What is the Empirical Rule in statistics?

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 is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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 weight of babies is 7.5 lbs and the standard deviation is 1 lb, what is the range for one standard deviation from the mean?

Back

The range is from 6.5 lbs to 8.5 lbs.

Front

How do you find the area under the normal curve?

Back

The area under the normal curve can be found using z-scores and standard normal distribution tables or calculators.

Front

What does it mean if a z-score is positive?

Back

A positive z-score indicates that the value is above the mean.

Front

What does it mean if a z-score is negative?

Back

A negative z-score indicates that the value is below the mean.

Front

If the shaded area under the curve is 0.85, what is the area to the left of the mean?

Back

The area to the left of the mean is 0.15.