Normal Distribution and Standard Deviation

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 often referred to as a 'bell curve'.

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.

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.

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.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

If the mean of a dataset is 50 and the standard deviation is 5, what is the range for 68% of the data?

Back

The range for 68% of the data is from 45 to 55.

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, and 99.7% within three standard deviations from the mean.

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 tell you?

Back

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