Normal Distribution

Front

What is a Normal Distribution?

Back

A Normal Distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What are the key parameters of a Normal Distribution?

Back

The key parameters of a Normal Distribution are the mean (μ), which indicates the center of the distribution, and the standard deviation (σ), which measures the spread or dispersion of the distribution.

Tags

CCSS.6.SP.A.3

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, 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 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.

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates the value is above the mean, while a negative z-score indicates it is below the mean.

Front

What is the significance of the 50th percentile in a Normal Distribution?

Back

The 50th percentile, also known as the median, is the value that separates the higher half from the lower half of the data set. In a normal distribution, it is equal to the mean.

Tags

CCSS.HSS.ID.A.4

Front

What is the area under the curve in a Normal Distribution?

Back

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

Front

How do you find the percentage of data below a certain value in a Normal Distribution?

Back

To find the percentage of data below a certain value, calculate the z-score for that value and then use the standard normal distribution table (z-table) to find the corresponding area.

Tags

CCSS.HSS.ID.A.4

Front

What is the relationship between mean, median, and mode in a Normal Distribution?

Back

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What is a standard normal distribution?

Back

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Tags

CCSS.HSS.ID.A.4