Normal Curve, Area and Z-Scores

Front

What is the normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It is calculated as Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What percentage of scores are greater than a Z-score of 1?

Back

Approximately 84% of scores are greater than a Z-score of 1 in a normal distribution.

Front

What does a Z-score of 0 represent?

Back

A Z-score of 0 represents a value that is exactly equal to the mean of the distribution.

Front

How do you calculate the area under the normal curve?

Back

The area under the normal curve can be calculated using Z-scores and standard normal distribution tables or software.

Front

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

Back

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

Front

What is the mean of a normal distribution?

Back

The mean of a normal distribution is the central value around which the data is distributed.

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 in a normal distribution.

Front

What is the significance of the 75th percentile?

Back

The 75th percentile indicates that 75% of the data points fall below this value.

Front

How do you find a score given a Z-score?

Back

To find a score given a Z-score, use the formula X = μ + Zσ, where μ is the mean and σ is the standard deviation.