Normal Distributions

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of the data falls within one standard deviation of the mean.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

How do you calculate the z-score for a given value?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score of 1.33 indicate?

Back

A z-score of 1.33 indicates that the value is 1.33 standard deviations above the mean.

Front

What is the 75th percentile?

Back

The 75th percentile is the value below which 75% of the data falls.

Tags

CCSS.6.SP.B.5C

Front

How do you find the percentile rank of a value in a data set?

Back

Percentile rank = (Number of values below X / Total number of values) * 100.

Tags

CCSS.6.SP.B.5C

Front

What is the area under the standard normal distribution curve?

Back

The total area under the standard normal distribution curve is 1.

Front

What does it mean if a score is at the 55th percentile?

Back

It means that 55% of the scores in the distribution are the same or lower than that score.

Tags

CCSS.6.SP.A.2

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 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Tags

CCSS.HSS.ID.A.4