# Thread: Help with Chebyshev's theorm!

1. ## Help with Chebyshev's theorm!

From years of experience fishing for trout in the Yellowstone River you know that the mean length of trout you catch is 14.7 inches with a standard deviation of 1.5 inches.
A) Use Chebyshev's Theorm to find an interval A to B for the lengths of trout in which at least 75% of the fish you catch will fall.
B)Compute the CV for this data.

2. Originally Posted by erikakillafornia
From years of experience fishing for trout in the Yellowstone River you know that the mean length of trout you catch is 14.7 inches with a standard deviation of 1.5 inches.
A) Use Chebyshev's Theorm to find an interval A to B for the lengths of trout in which at least 75% of the fish you catch will fall.
B)Compute the CV for this data.
Remember what Chubby Checkers says: Disregarding distribution, the percentage of values laying within K standard deviations from the mean will be $\displaystyle 1 - \frac{1}{K^2}$, for K greater than 1. Therefore, you can use Chubby's theorem to set up an equation:

$\displaystyle .75 = 1 - \frac{1}{K^2}$

And solve for K, which will give you how many standard deviations (to the left and right), a certain value is. These values will be the interval that corresponds to 75% of the data laying within K standard deviations of the mean.

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