Normal Distribution Unit Review 1

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, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center point of a normal distribution.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean.

Front

How do you find 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 is the total area under the normal distribution curve?

Back

The total area under the normal distribution curve is equal to 1.

Front

What percentage of data falls within 1 standard deviation of the mean according to the empirical rule?

Back

Approximately 68% of the data falls within 1 standard deviation of the mean.

Front

How do you calculate the probability of a value being less than a certain number in a normal distribution?

Back

You can calculate this using the z-score and then referring to the standard normal distribution table.

Front

What is the significance of the top 22% in a normal distribution?

Back

The top 22% refers to the values that are greater than the 78th percentile of the distribution.

Front

If the mean is 10 and variance is 4, what is the standard deviation?

Back

The standard deviation is the square root of the variance, so it is 2.