
Empirical Rule and Normal Distributions Flashcard
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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16 questions
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1.
FLASHCARD QUESTION
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.
2.
FLASHCARD QUESTION
Front
How do you calculate the z-score?
Back
The z-score is calculated using the formula: z = (x - mean) / standard deviation, where x is the value for which you are calculating the z-score.
3.
FLASHCARD QUESTION
Front
What percentage of data lies below the mean in a normal distribution?
Back
In a normal distribution, 50% of the data lies below the mean.
4.
FLASHCARD QUESTION
Front
If a normal distribution has a mean of 100 and a standard deviation of 15, what is the z-score for a value of 130?
Back
The z-score is calculated as z = (130 - 100) / 15 = 2.
5.
FLASHCARD QUESTION
Front
What does a z-score of 0 indicate?
Back
A z-score of 0 indicates that the value is exactly equal to the mean of the distribution.
6.
FLASHCARD QUESTION
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.
7.
FLASHCARD QUESTION
Front
In a normal distribution, what percentage of data falls within two standard deviations of the mean?
Back
Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.
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