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?

Back

The Empirical Rule states that for a normal distribution: approximately 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 percentage of data falls between the mean and one standard deviation above the mean in a normal distribution?

Back

Approximately 34% of the data falls between the mean and one standard deviation above the mean in a normal distribution.

Tags

CCSS.HSS.ID.A.4

Front

What is the significance of the standard deviation in a normal distribution?

Back

The standard deviation 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, while a larger standard deviation indicates a wider spread.

Front

How do you find the area under the normal curve?

Back

The area under the normal curve can be found using z-scores and standard normal distribution tables, or by using statistical software or calculators that provide cumulative distribution functions.

Tags

CCSS.HSS.ID.A.4

Front

What is the relationship between the mean and median in a normal distribution?

Back

In a normal distribution, the mean and median are equal, as the distribution is symmetric around the mean.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

How do you determine the cutoff value for a specific percentile in a normal distribution?

Back

To determine the cutoff value for a specific percentile, you can use the z-score corresponding to that percentile and the formula: X = μ + z * σ.

Tags

CCSS.HSS.ID.A.4

Front

What is the probability of a value being greater than the mean in a normal distribution?

Back

The probability of a value being greater than the mean in a normal distribution is 50%.

Tags

CCSS.HSS.ID.A.4

Front

What does it mean if a score is in the top 10% of a normal distribution?

Back

A score in the top 10% means that it is higher than 90% of the scores in the distribution, indicating it is significantly above average.

Tags

CCSS.HSS.ID.A.4