Use of Chebyshevs inequality?

[perdition]

I am aware of sd and % of population sample for a normal distribution 1=68, 2=95 & 3=99.
Brushing up on a few concepts, I realise Chebyshev can be used on any shape of distribution, and the sd to proportion of sample mean for a sample/population are different, e.g. 2 sd = 75%
From the point of view of the exam, what do I need to know, as in why use Chebyshev……will it state under Chebyshev inequality etc….
I would think in terms of the normal distribution relationship first, hopefully I am missing something very basic here as to when you would use either format….cheers.

 

[JoeyDVivre]

Chebyshev is an inequality while the normal distriibution quantiles are exact. That means that a Chebyshev question needs to contain terms like “at least” and there is no mention of normality. For example,
The mean tax refund for Americans is $800 with a standard deviation of $200. What probabilistic statement can you make about the percentage of Americans receiving tax refunds between $400 and $1200?
a) At least 50%
b) At least 75%
c) Can’t say anything
d) 95%
Answer is B, because it has the “at least” and there is no mention of normality (or other distribution) in the question.

 

[perdition]

Thanks Joey, that helps…..think normal distribution, unless you have reason not to..Tks!