Applied Math - Statistics - Flashcard 2 - Normal Curves

Front

What is a normal curve?

Back

A normal curve is a bell-shaped graph that represents a normal distribution, where most of the data points cluster around the mean, and the probabilities for values further away from the mean taper off equally in both directions.

Front

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

Back

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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 in a normal distribution.

Front

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

Back

Approximately 99.7% of the data falls within three standard deviations of the mean in a normal distribution.

Front

If the mean of a normally distributed dataset is 50 and the standard deviation is 10, what is the range for 68% of the data?

Back

The range for 68% of the data is from 40 to 60.

Front

What is the empirical rule in statistics?

Back

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

Front

How do you find the z-score for a value in a normal distribution?

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 of 0 indicate?

Back

A z-score of 0 indicates that the value is exactly equal to the mean of the distribution.

Front

In a normal distribution, what does it mean if a value has a negative z-score?

Back

A negative z-score indicates that the value is below the mean of the distribution.

Front

In a normal distribution, what does it mean if a value has a positive z-score?

Back

A positive z-score indicates that the value is above the mean of the distribution.