Hi, I’m confused on testing/verifying Chebyshev’s theorem, thought I did it in first pic but comment from my professor stated otherwise. Using the data above, kindly help verify Chebyshev’s theorem ### Sample Data Analysis#### Graph DescriptionThe graph titled "Sample Data" is a vertical bar chart displaying 30 data points. The x-axis represents samples numbered from 1 to 30, while the y-axis represents their corresponding values, ranging from 0 to 120. The bars vary in height, showing the distribution of data values across these samples.#### Statistical AnalysisFrom the graph given above, the mean is calculated as follows:\[ \text{Mean} = \frac{1908.42}{30} = 63.6 \]The standard deviation (Sd) is:\[ \text{Sd} = 18.8 \]#### Probability CalculationsUsing Chebyshev's inequality, the probability \( P(|x - \mu| \geq k\sigma) \) satisfies:\[ P(|x - \mu| \geq k\sigma) \leq \frac{1}{k^2} \]Let’s assume \( k \) to be 1.5, 2, and 3:1. **For \( k = 1.5 \):** \[ \begin{align*} 63.6 - (1.5)(18.8) &= 63.6 - 28.2 = 35.4 \\ 63.6 + (1.5)(18.8) &= 63.6 + 28.2 = 91.8 \\ \end{align*} \]2. **For \( k = 2 \):** \[ \begin{align*} 63.6 - (2)(18.8) &= 63.6 - 37.6 = 26 \\ 63.6 + (2)(18.8) &= 63.6 + 37.6 = 101.2 \\ \end{align*} \]3. **For \( k = 3 \):** \[ \begin{align*} 63.6 - (3)(18.8) &= 63.6 - 56.4 = 7.2 \\ 63.6 + (3)(18.8) &= 63.6 + 56.4 = 120 \\ \end{align*} \] You have not done the two examples I asked you to do, (k=2 and 3), to verify Chebyshev's theorem.The example you did was a process to find the value of k when the probability of the inequality is 100% which is a good practice as long as you state the purpose of the example clearly.Once we overcome the mathematical hurdle, we all move to data analysis.

Chebyshev's theorem: Let X be a random variable with mean μ and standard deviation σ then for any…

Answered: Using the data above, kindly help…

Using the data above, kindly help verify Chebyshev’s theorem

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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