FRI. ET: 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 is the empirical rule?

Back

The empirical rule states that for a normal distribution: 68% of the 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 standard deviation measure?

Back

Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

If the mean is 80 and the standard deviation is 4, what is the score that is 1 standard deviation above the mean?

Back

84

Front

In a normal distribution, what percentage of data falls within 2 standard deviations of the mean?

Back

95%.

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

If a score of 75 is 1 standard deviation below the mean, what is the mean if the standard deviation is 5?

Back

80.

Front

What is the range of scores that includes approximately 68% of the data if the mean is 50 and the standard deviation is 10?

Back

40 to 60.

Front

How do you find the mean from a given score and standard deviation?

Back

Add the score to the standard deviation for scores above the mean or subtract for scores below the mean.

Front

What is the significance of the area under the normal distribution curve?

Back

The area under the curve represents the total probability of all outcomes, which equals 1.