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