IB Math Applications Normal distribution

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
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14 questions
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1.
FLASHCARD QUESTION
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).
2.
FLASHCARD QUESTION
Front
What percentage of data falls within one standard deviation of the mean in a normal distribution?
Back
Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ) in a normal distribution.
3.
FLASHCARD QUESTION
Front
What percentage of data falls within two standard deviations of the mean in a normal distribution?
Back
Approximately 95% of the data falls within two standard deviations (2σ) of the mean (μ) in a normal distribution.
4.
FLASHCARD QUESTION
Front
What percentage of data falls within three standard deviations of the mean in a normal distribution?
Back
Approximately 99.7% of the data falls within three standard deviations (3σ) of the mean (μ) in a normal distribution.
5.
FLASHCARD QUESTION
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.
6.
FLASHCARD QUESTION
Front
What is the significance of the z-score in a normal distribution?
Back
The z-score indicates how many standard deviations a data point is from the mean. It helps in determining the probability of a value occurring within a normal distribution.
7.
FLASHCARD QUESTION
Front
If the mean waist size is 29 inches and the standard deviation is 1.4 inches, what is the z-score for a waist size of 31 inches?
Back
The z-score for a waist size of 31 inches is calculated as: z = (31 - 29) / 1.4 = 1.43.
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