1. ## Tchebysheff's Theorem

Here's my question : The U.S Mint produces dimes with an average diameter of .5 inch and standard deviation .01. Using Tchebysheff's theorem, find a lower bound for the number of coins in a lot of 400 coins that are expected to have a diameter between .48 and .52.

-I just really am lost on this problem, anyone able to help?

2. Originally Posted by mathlete2
Here's my question : The U.S Mint produces dimes with an average diameter of .5 inch and standard deviation .01. Using Tchebysheff's theorem, find a lower bound for the number of coins in a lot of 400 coins that are expected to have a diameter between .48 and .52.

-I just really am lost on this problem, anyone able to help?
Tchebysheff's or Chebyshev's inequality is:

$P(|X-\mu|>k\sigma )\le \frac{1}{k^2}$

In the case of the dimes we are being asked for bound on:

$P(|X-\mu|\le 2\sigma )=1-P(|X-\mu|> 2\sigma) \ge 1-\frac{1}{4}$

RonL