Normal Distribution - Empirical Rule

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 percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68%

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95%

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

99.7%

Front

If the mean age of golfers is 38 and the standard deviation is 4, what is the age range for the middle 68% of golfers?

Back

34 to 42 years old.

Front

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

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the 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 does it mean if data is skewed right?

Back

If data is skewed right, it means that the tail on the right side of the distribution is longer or fatter than the left side, indicating that there are a larger number of lower values.

Front

In a normal distribution, what is the area under the curve equal to?

Back

1 (or 100%)

Front

What is the significance of the mean in a normal distribution?

Back

The mean is the central point of the distribution, where the highest frequency of data points occurs.