z-Scores and Normal Distributions

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean of a data set.

Front

How do you calculate a z-score?

Back

The formula for calculating a z-score is: z = (X - μ) / σ, where X is the value, μ is the mean, 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

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution and is located at the center of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that in a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Front

What is the area under the normal curve?

Back

The total area under the normal distribution curve is equal to 1, representing the total probability.

Front

What is InvNorm?

Back

InvNorm is a function used to find the z-score that corresponds to a given cumulative probability in a normal distribution.

Front

How do you find the probability of a z-score?

Back

You can find the probability of a z-score using a z-table or a calculator that provides cumulative probabilities.