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

Front

What happens to the mean and median when an outlier is added to the right of a normal distribution?

Back

The mean will be greater than the median (mean > median).

Front

If the mean of a normal distribution is 30 and the standard deviation is 5, what is the value at one standard deviation below the mean?

Back

25.

Front

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

Back

95%.

Front

What does it mean if a distribution is skewed to the left?

Back

A left-skewed distribution has a longer tail on the left side, meaning that the majority of the data points are concentrated on the right.

Front

In a normal distribution, what is the relationship between the mean, median, and mode?

Back

In a normal distribution, the mean, median, and mode are all equal.

Front

What is the standard deviation?

Back

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

Front

If a dairy product has a mean shelf life of 12 days and a standard deviation of 3 days, what percentage of products last between 12 and 15 days?

Back

34%.

Front

What is the z-score?

Back

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