Normal Distributions: Empirical Rule Practice

Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

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 one standard deviation of the mean in a normal distribution?

Back

68%.

Front

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

Back

95%.

Front

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

Back

99.7%.

Front

If the mean is 38 and the standard deviation is 4, what is the range for one standard deviation?

Back

34 to 42.

Front

If the mean is 12 and the standard deviation is 3, what is the percentage of products that last between 12 and 15 days?

Back

34%.

Front

What is the z-score formula?

Back

The z-score formula is z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

How do you find the proportion of data between two values in a normal distribution?

Back

Use the z-scores for both values to find the corresponding probabilities from the standard normal distribution table.

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.