Finding Z - Score

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It 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

How do you calculate a Z-score?

Back

To calculate a Z-score, use the formula: Z = (X - μ) / σ, where X is the value for which you want to find the Z-score, μ is the mean of the dataset, and σ is the standard deviation.

Front

What does a positive Z-score indicate?

Back

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

Front

What does a negative Z-score indicate?

Back

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

Front

If the mean is 30 and the standard deviation is 5, what is the Z-score for X = 35?

Back

Z = (35 - 30) / 5 = 1.0.

Front

If the mean is 50 and the standard deviation is 10, what is the Z-score for X = 40?

Back

Z = (40 - 50) / 10 = -1.0.

Front

What is the significance of a Z-score of 0?

Back

A Z-score of 0 indicates that the value is exactly equal to the mean.

Front

How does the Z-score relate to the standard normal distribution?

Back

The Z-score transforms any normal distribution into the standard normal distribution, which has a mean of 0 and a standard deviation of 1.

Front

What is the Z-score for a value that is 2 standard deviations above the mean?

Back

The Z-score would be +2.

Front

What is the Z-score for a value that is 3 standard deviations below the mean?

Back

The Z-score would be -3.