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Solving using Chebyshev's theorem

nickar1172

New member
Dec 11, 2013
20
how do you solve this problem?

Average of one slice contains 0.260 milligrams of vitamin b, with a standard deviation of 0.005 milligrams. According to Chebyshev's theorem, between what values must the thiamine content be of

a) at least 35/36 of all slices of this bread
b)at least 80/81 of all slices of this bread

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is the answer for a) 6 and b) 9???
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,854
how do you solve this problem?

Average of one slice contains 0.260 milligrams of vitamin b, with a standard deviation of 0.005 milligrams. According to Chebyshev's theorem, between what values must the thiamine content be of

a) at least 35/36 of all slices of this bread
b)at least 80/81 of all slices of this bread

- - - Updated - - -

is the answer for a) 6 and b) 9???
Hi nickar1172! :)

The question ask "between what values", meaning you're supposed to answer each question with a lower bound and an upper bound.

From Chebyshev's theorem $\Pr(|X-\mu|\geq k\sigma) \leq \frac{1}{k^2}$, I do get that $k=6$ for (a) and $k=9$ for (b).

But that's an intermediate result that does not answer the question yet...