# Thread: Chebyshev's theorem and empirical rule

1. ## Chebyshev's theorem and empirical rule

can someone please explain how to do this problem? I am so confused!

Assume the distribution of weights of US adults are normally distributed with mean = 162 lbs and standard deviation= 23 lbs. Find the following probability P (127.5 <x > 196.5) using chebyshev's theorem.

THank you!!

2. Originally Posted by vintageglam09
can someone please explain how to do this problem? I am so confused!

Assume the distribution of weights of US adults are normally distributed with mean = 162 lbs and standard deviation= 23 lbs. Find the following probability P (127.5 <x > 196.5) using chebyshev's theorem.

THank you!!

Prob{127.5 <x > 196.5} = 0.5555555... using chebyshev's theorem...yawn.

3. You can not find the actual value of probability using chebyshev's theorem, because it is an inequality. It will give only an upper bound or lower bound of a probability.

4. Oh darn...The question implies what fraction of the set of measurements (weights) lie between -1.5 and +1.5 standard deviatons of the mean. Using Chebyshev's theorem the answer is:

at least 1-1/k^2 = 1 - 1/(1.5)^2 = 0.5555...

Now how's that?

Just an added follow-up note: Why would someone want to use Chebyshev's theorem if it is known that the underlying distribution is normal?

5. The answer is at least 0.55, which means 0.55 is the lower bound of the probability.

Chebyshev's theorem is usually using only if the distribution of the random variable is unknown.

6. Yep, my thoughts too. It looks like someone put together two different questions. Obviously, the probability can be easily computed using the unit normal distribution.

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