Chapter 5 Normal Distribution Probabilities 2023

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. It is defined by its mean (μ) and standard deviation (σ).

Front

What does the mean represent in a normal distribution?

Back

The mean (μ) represents the average value of the data set and is the center of the normal distribution curve.

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Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation (σ) measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that for a normal distribution: about 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.

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CCSS.HSS.ID.A.4

Front

How do you calculate the z-score?

Back

Front

What is the significance of the z-table?

Back

The z-table provides the area (probability) to the left of a given z-score in a standard normal distribution, allowing for the calculation of probabilities.

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CCSS.HSS.ID.A.4

Front

What is the probability of a z-score being less than a certain value?

Back

To find the probability of a z-score being less than a certain value, refer to the z-table to find the corresponding area under the curve.

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CCSS.HSS.ID.A.4

Front

How do you find the probability of a sample mean?

Back

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CCSS.HSS.ID.A.4

Front

What is the 75th percentile in a normal distribution?

Back

The 75th percentile is the value below which 75% of the data falls. It can be found using the z-score corresponding to 0.75 in the z-table.

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CCSS.HSS.ID.A.4

Front

How do you determine the value corresponding to a specific percentile?

Back

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