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 data falls within one standard deviation of the mean.

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, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate a z-score?

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 represent?

Back

A z-score indicates how many standard deviations a data point is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is the significance of the area under the normal curve?

Back

The area under the normal curve represents the probability of a value falling within a certain range. The total area is equal to 1.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

How do you find the percentile rank of a score?

Back

Percentile rank is found by determining the percentage of scores that fall below a given score in a distribution.

Tags

CCSS.6.SP.B.5C

Front

What is the relationship between z-scores and percentiles?

Back

Z-scores can be used to find percentiles in a normal distribution by determining the area to the left of the z-score.

Tags

CCSS.HSS.ID.A.4

Front

What is the standard normal distribution?

Back

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

Tags

CCSS.HSS.ID.A.4

Front

How do you interpret a z-score of -3?

Back

A z-score of -3 indicates that the value is 3 standard deviations below the mean, which is very rare in a normal distribution.

Tags

CCSS.HSS.ID.A.4