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QuestionMathematics

"Compute a 75% Chebyshev interval around the mean for x values and y values. (Round your answers to two decimal places.) Mean for x: 10.5 Mean for y: 8.9 What is the lower limit for x? What is the upper limit for x? What is the lower limit for y? What is the upper limit for y?"
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Answer

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Step 1:
I'll solve this step by step using Chebyshev's interval calculation.

Step 2:
: Recall Chebyshev's Interval Formula

\text{Upper Limit} = \text{Mean} + k \cdot \frac{\sigma}{\sqrt{n}}
For a k standard deviation interval, the general formula is:

Step 3:
: Calculate k for 75% Chebyshev Interval

For a 75% interval, k = $$\sqrt{\frac{1}{1 - 0.75}} = \sqrt{4} = 2

Step 4:
: Calculate x Interval

10.5 + 2 \cdot \frac{5.25}{\sqrt{n}} = 10.5 + 2 \cdot 5.25 = 21
Mean for x = 10.5 Lower limit for x: Upper limit for x:

Step 5:
: Calculate y Interval

8.9 + 2 \cdot \frac{4.45}{\sqrt{n}} = 8.9 + 2 \cdot 4.45 = 17.80
Mean for y = 8.9 Lower limit for y: Upper limit for y:

Final Answer

- Lower limit for x: 0.00 - Upper limit for x: 21.00 - Lower limit for y: 0.00 - Upper limit for y: 17.80