# Solving using Chebyshev's theorem

#### nickar1172

##### New member
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
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...