Normal Distribution & Empirical Rule &Z scores

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

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It is calculated as Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

Calculate the Z-score for x = 29, Mean = 22, Standard Deviation = 3.1.

Back

Z = (29 - 22) / 3.1 = 2.26.

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

What is the disadvantage of the Empirical Rule?

Back

The data has to be approximately normal.

Front

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

Back

34%.

Front

Calculate the Z-score for x = 2 from the data set {7, 9, 9, 12, 5, 3, 15, 8}.

Back

Z = (2 - 8) / 3.24 = -1.86.