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 does the mean represent 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 curve.

Front

What is the standard deviation in a normal distribution?

Back

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

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% within two standard deviations, and 99.7% within three standard deviations.

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 the majority of the data points are concentrated on the right.

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the total probability of all outcomes, which equals 1.

Front

How do you find the z-score?

Back

The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation: z = (X - μ) / σ.

Front

What is a quartile?

Back

A quartile is a type of quantile that divides a ranked dataset into four equal parts, with each part representing a fourth of the data.

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations of the mean.

Front

What is the relationship between the mean, median, and mode in a normal distribution?

Back

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.