Z-scores, Percentiles and Empirical Rule

What is the formula for calculating z-scores?

• (x - μ) * σ

• (x + μ) / σ

• (x - μ) / σ

• (x + μ) * σ

A data set follows a normal distribution. What percentage of the data falls within one standard deviation of below the mean and the mean

• 90%

• 95%

• 68%

• 34%

If a data set has a mean of 50 and a standard deviation of 10, what is the z-score for a data point of 60?

• 0.5

• 2

• 5

• 1

What is the range of z-scores that fall within two standard deviations of the mean according to the empirical rule?

• -1 to +1

• -2 to +2

• -4 to +4

• -3 to +3

What is the percent of data that fall within two standard deviations of the mean according to the empirical rule?

• 95%

• 99.7%

• 68%

• 2.35%

What is the approximate percentage of data that falls within three standard deviations of the mean according to the empirical rule?

• 99.7%

• 90%

• 85%

• 95%

What is the approximate percentage of data that falls within below a z-score of -3

• 99.7%

• 90%

• 2.5%

• 95%

If a data set has a mean of 75 and a standard deviation of 5, what is the z-score for a data point of 80?

• 1

• 2

• 10

• 0.5

What is the relationship between z-scores and percentiles?

• Z-scores and percentiles are unrelated measures.

• Z-scores and percentiles are both measures of relative position in a distribution.

• Z-scores are used to calculate percentiles.

• Percentiles are used to calculate z-scores.

If a data set is normally distributed, what percentage of the data falls within three standard deviations of the mean according to the empirical rule?

• 95%

• 90%

• 85%

• 99.7%