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 is the shape of a normal distribution curve?

Back

The shape of a normal distribution curve is called a bell curve.

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution: about 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 represents the average value of the data set and is the center of the normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation indicates the amount of variation or dispersion of a set of values. A smaller standard deviation means the data points are closer to the mean.

Front

If the mean is 38 and the standard deviation is 4, what is the z-score for a value of 34?

Back

The z-score is calculated as (X - mean) / standard deviation = (34 - 38) / 4 = -1.

Front

What percentage of data falls below the mean in a normal distribution?

Back

50% of the data falls below the mean 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 is the significance of a z-score of 0?

Back

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

Front

What does a negative z-score indicate?

Back

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