Normal Distribution Flashcard

Front

What is the empirical rule in statistics?

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

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68%

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95%

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

99.7%

Tags

CCSS.HSS.ID.A.4

Front

If a normal distribution has a mean of 30 and a standard deviation of 5, what value corresponds to 1 standard deviation below the mean?

Back

25

Front

In a normal distribution, what does the area under the curve represent?

Back

The area under the curve represents the total probability of all outcomes, which equals 1.

Front

What is the z-score formula?

Back

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

Front

If the ages of golfers are normally distributed with a mean of 38 and a standard deviation of 4, what percentage of golfers are between 30 and 46 years old?

Back

95%

Tags

CCSS.HSS.ID.A.4

Front

In a normal distribution, what does a z-score of 0 indicate?

Back

A z-score of 0 indicates that the value is exactly at the mean.

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.