QQuestionMathematics
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
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