7. Apply Chebyshev's Theorem to find the least possible fraction of the numbers in a data set lying within standard deviations of the mean. 7 standard deviations from the mean. At least of all numbers must lie within (Type an integer or a simplified fraction.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Title**: Applying Chebyshev's Theorem to Data Sets
**Instruction**: Use Chebyshev's Theorem to determine the minimum fraction of numbers in a data set that fall within \(\frac{7}{5}\) standard deviations of the mean.
**Problem Statement**:
At least [ ] of all numbers must lie within \(\frac{7}{5}\) standard deviations from the mean.
(Type an integer or a simplified fraction.)
**Answer Box**: Enter your answer in the box provided.
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**Explanation**: Chebyshev's Theorem is a statistical rule stating that the fraction of values within \(k\) standard deviations of the mean is at least \(1 - \frac{1}{k^2}\). Here, \(k\) is \(\frac{7}{5}\), and you need to calculate \(1 - \frac{1}{(\frac{7}{5})^2}\) to find the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96d4c8cb-af63-459c-8cdf-c777fdfe530a%2Ff3fe5a56-9e2b-4af5-bbdc-51ebbc6f3bf4%2Fmx0y8lj_processed.jpeg&w=3840&q=75)
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