The Normal Distribution Practice

Front

What is the normal distribution?

Back

The normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, defined by its mean (average) and standard deviation (spread). It describes how the values of a variable are distributed.

Front

What is the mean in a normal distribution?

Back

The mean is the average value of a set of data points in a normal distribution, and it is the center of the distribution curve.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation is a measure of the amount of variation or dispersion in a set of values. In a normal distribution, it determines the width of the curve.

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.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the percentage of data that falls outside a specified range in a normal distribution?

Back

To calculate the percentage of data that falls outside a specified range, you can use the cumulative distribution function (CDF) to find the probabilities of the lower and upper bounds, then subtract these from 1.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

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

Back

Approximately 99.7% of the data falls within three standard deviations of the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

How do you find the z-score for a value in a normal distribution?

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.

Tags

CCSS.HSS.ID.A.4

Front

What is a z-score?

Back

A z-score indicates how many standard deviations a data point is from the mean of the distribution. It can be positive or negative.