Z SCORES & EMPIRICAL RULE

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

In a normal distribution, what percent of the values lie above the mean?

Back

50%

Front

What is a z-score?

Back

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.

Front

How do you calculate a z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

If a score is 1/2 standard deviation above the mean, what is its z-score?

Back

+0.50

Front

If a score is 2 standard deviations below the mean, what is its z-score?

Back

-2.00

Front

In a normal distribution with μ=70 and σ=5, what percent of scores are greater than 75?

Back

16%

Front

How many standard deviations is a score of 80 from the mean in a normal distribution with μ=70 and σ=5?

Back

2 standard deviations above the mean.

Front

What is the area under the normal curve between the mean and one standard deviation above the mean?

Back

Approximately 34%.

Front

In a normal distribution, what percent of scores lie between the mean and two standard deviations above the mean?

Back

Approximately 97.5%.