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Consider a zoo with two animals: an elephant and a lion. The elephant's expected lifespan is $70$ years, but it lives to be $65$ years ($SD = 7$). Likewise, the lion's expected lifespan is $22$ years, but it lives to be $28$ years ($SD = 3$).

Could anyone explain why statistics tells us that the lion had a longer lifespan relative to the elephant?

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closed as unclear what you're asking by Did, Najib Idrissi, 91500, drhab, mrf Sep 25 '15 at 14:06

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

    
"Statistics" tells us that? How? I would say statistics tells us nothing here. – Did Oct 7 '13 at 8:05

I am assuming you are asking if statistics could tell us why the Z-score (i.e., $\frac{Actual\;Lifespan - Mean\;Lifespan}{SD}$) for the elephant is -0.7 while the Z-score for the lion is 2.0. Now, the whole point of statistics is that we are assuming we $\textit{cannot}$ predict individual outcomes, only aggregate properties. So, as Did mentioned in the above comment, statistics does $\textit{not}$ tell us why this particular elephant lived shorter than expected while the lion lived longer than expected. You would need an autopsy by a forensic veterenarian or biologist to determine the exact cause (perhaps the elephant had cancer and the lion was born of long lived parents).

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The lion lives longer than expected, while the elephant lives shorter than expected, so one could say that the lion has had a relatively longer lifespan. Although it is hard to tell what is really being asked without a precise definition of a 'relatively longer lifespan'.

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statistics tell us the Z-score (i.e., $\frac{Actual\;Lifespan - Mean\;Lifespan}{SD}$) for the elephant is -0.7 while the Z-score for the lion is 2.0.

we're assuming a normal distribution and a Z score of 2.0 means that it lived longer than 97.5% of the other lions while the elephant lived only ~ 40% longer than the other elephants (look up 68-95-99.7 rule)

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