Normal distribution

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 mean in a normal distribution?

Back

The mean is the average of all data points in a normal distribution, and it is located at the center 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 does the empirical rule state?

Back

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

Front

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

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 (X - mean) / standard deviation.

Front

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

Back

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

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

What is the significance of the area under the curve between z = 0 and z = 1.45?

Back

It represents the probability of a score falling between the mean and 1.45 standard deviations above the mean.

Front

What does it mean if a distribution is skewed to the left?

Back

A left-skewed distribution has a longer tail on the left side, indicating that there are a larger number of lower values.