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 are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of data falls within one standard deviation of the mean.

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 one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of 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 amount of variation or dispersion of a set of values in a normal distribution.

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 of the distribution.

Front

What percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34% of data falls between the mean and one standard deviation above the mean.

Front

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

Back

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

Front

What is the probability of a z-score greater than 2 in a normal distribution?

Back

The probability of a z-score greater than 2 is approximately 2.5%.