Normal Distributions Application

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

Front

What does the mean represent in a normal distribution?

Back

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

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

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

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

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

Back

Approximately 99.7%.

Front

How do you calculate the z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score tell you?

Back

A z-score indicates how many standard deviations an element is from the mean.

Front

If a dataset has a mean of 50 and a standard deviation of 10, what is the z-score of a value 70?

Back

Z-score = (70 - 50) / 10 = 2.