Normal Distribution and 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 is the empirical rule?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average of all data points and is the center of the normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

If the mean is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of the data?

Back

28,000 km to 32,000 km.

Front

If the mean is 1150 pounds and the standard deviation is 22 pounds, what is the range for 95% of the data?

Back

1106 pounds to 1194 pounds.

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

Given a mean of 15 and a standard deviation of 3, what interval shows 95% of the data?

Back

9 to 21.