Normal Distributions Mixed Practice

Front

What is a 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 the empirical rule?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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 does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the data point is above the mean, while a negative z-score indicates it 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 the center point of the distribution.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation is a measure of the amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

Front

What is the 75th percentile?

Back

The 75th percentile is the value below which 75% of the data falls. It is a measure of relative standing in a data set.

Front

How do you find the 75th percentile in a normal distribution?

Back

To find the 75th percentile, you can use the mean and standard deviation along with z-scores from the standard normal distribution table.

Front

What is the probability of a score being less than a certain value in a normal distribution?

Back

The probability can be found using the z-score and the standard normal distribution table to determine the area under the curve to the left of that z-score.

Front

What is the significance of the area under the curve in a normal distribution?

Back

The area under the curve represents the total probability of all outcomes, which equals 1 (or 100%).