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 1 standard deviation of the mean, about 95% falls within 2 standard deviations, and about 99.7% falls within 3 standard deviations.

Front

What percentage of data falls within 1 standard deviation of the mean according to the empirical rule?

Back

68%

Front

How do you calculate the 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

What is a z-score?

Back

A z-score indicates how many standard deviations a data point is from the mean of a distribution.

Front

Given a mean of 75 and a standard deviation of 7, what is the z-score for a score of 82?

Back

The z-score is 1.

Front

What is the mean and standard deviation of a normal distribution?

Back

The mean is the average of the data, and the standard deviation measures the spread of the data around the mean.

Front

If the mean is 100 and the standard deviation is 15, what is the range of values within 1 standard deviation?

Back

The range is from 85 to 115.

Front

In a normal distribution, what does it mean if a score has a negative z-score?

Back

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

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion of data points from the mean; a smaller standard deviation indicates that the data points are closer to the mean.

Front

If the average height of men is 70 inches with a standard deviation of 3 inches, what is the z-score for a man who is 67 inches tall?

Back

The z-score is -1.