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 the mean, median, and mode are all equal. It is defined by its mean (μ) and standard deviation (σ).

Front

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

Back

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

Tags

CCSS.HSS.ID.A.4

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.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What does the standard deviation represent 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

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

Back

Tags

CCSS.HSS.ID.A.4

Front

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

Back

The z-score indicates how many standard deviations a value (X) is from the mean. A positive z-score means the value is above the mean, while a negative z-score means it is below the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you find the probability of a range of values in a normal distribution?

Back

To find the probability of a range of values, calculate the z-scores for both values, then use the standard normal distribution table (z-table) to find the probabilities corresponding to those z-scores and subtract them.

Tags

CCSS.HSS.ID.A.4

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 possible outcomes.

Front

What is the middle 30% of a normal distribution?

Back

The middle 30% of a normal distribution refers to the range of values that fall between the 35th percentile and the 65th percentile.

Tags

CCSS.HSS.ID.A.4

Front

How do you determine the lightest 22% of cans in a normal distribution?

Back

Tags

CCSS.HSS.ID.A.4