Relationship between expected and actual value

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

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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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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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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