Normal Distribution & Empirical Rule

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 shape does a normal distribution curve have?

Back

A normal distribution curve has a bell shape.

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

If the mean is 38 and the standard deviation is 4, what percentage of data falls between 34 and 42?

Back

68% of the data falls between 34 and 42.

Front

How do you calculate the percentage of data above a certain value in a normal distribution?

Back

Use the z-score formula: z = (X - mean) / standard deviation, then refer to the standard normal distribution table.

Front

What is a z-score?

Back

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

Front

In a normal distribution, what percentage of data falls within two standard deviations of the mean?

Back

Approximately 95% of the data falls within two standard deviations of the mean.

Front

If a normal distribution has a mean of 1150 and a standard deviation of 22, what is the range for 95% of the data?

Back

The range for 95% of the data is approximately 1106 to 1194 pounds.

Front

What does it mean if a golfer is older than 42 in a normal distribution with a mean of 38 and a standard deviation of 4?

Back

It means that the golfer is more than one standard deviation above the mean.

Front

How do you find the proportion of data below a certain value in a normal distribution?

Back

Calculate the z-score for that value and use the standard normal distribution table to find the corresponding proportion.