Modeling with Normal Distributions

Modeling with Normal Distributions

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

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14 questions

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1.

FLASHCARD QUESTION

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).

2.

FLASHCARD QUESTION

Front

What does the mean represent in a normal distribution?

Back

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

3.

FLASHCARD QUESTION

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. A smaller standard deviation indicates that the data points are closer to the mean.

4.

FLASHCARD QUESTION

Front

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

Back

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

5.

FLASHCARD QUESTION

Front

How do you calculate the z-score?

Back

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

6.

FLASHCARD QUESTION

Front

What is the significance of the z-score in normal distributions?

Back

The z-score indicates how many standard deviations a data point is from the mean. It helps in determining the probability of a value occurring within a normal distribution.

7.

FLASHCARD QUESTION

Front

What is the area under the normal distribution curve?

Back

The total area under the normal distribution curve is equal to 1, representing the total probability of all outcomes.

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