Normal Distributions Review

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It 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 it mean to be at the 55th percentile?

Back

Being at the 55th percentile means that 55% of the data points are equal to or below your score.

Tags

CCSS.6.SP.A.2

Front

How do you calculate a score from a Z-score?

Back

To find the score (X) from a Z-score, use the formula X = μ + Z * σ, where μ is the mean and σ is the standard deviation.

Tags

CCSS.HSS.ID.A.4

Front

What is the mean and standard deviation of a standard normal distribution?

Back

In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Front

What is the shape of a normal distribution?

Back

A normal distribution is bell-shaped and symmetric about the mean.

Front

What does it mean if a distribution is unimodal?

Back

A unimodal distribution has one clear peak or mode, indicating the most frequent value.

Front

What is the significance of the 75th percentile?

Back

The 75th percentile indicates that 75% of the data points fall below this value.

Tags

CCSS.6.SP.B.5C

Front

How do you find the Z-score for a given value?

Back

To find the Z-score, subtract the mean from the value and then divide by the standard deviation: Z = (X - μ) / σ.

Front

What is the Z-score for a player who runs a time of 5.6 seconds if the mean is 5.2 seconds and the standard deviation is 0.3 seconds?

Back

Z = (5.6 - 5.2) / 0.3 = 1.33.

Front

What is the formula for calculating the Z-score?

Back

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