求解Prep统计题 (DS)

cherry_rui

The lifetime of all the batarries produced by a certain company in a year have a distribution that is a symmetric about the mean m. If the distribution has a standard deviation of d, what is the percenage is greater than m+d?
(1)68% of the distribution lies in the interval from m-d to m+d, inclusive.
(2)16% of the distribution is less than m-d.

sunflower88

If you know the meaning of "a distribution that is a symmetric about the mean m", then you would choose D since both conditions are sufficient.

cherry_rui

不好意思，这句没明白，能解释一下吗？

zhongyaya

用google找的解释（2）：

the poster above did a good job of explaining the significance of the symmetry statement, so i don't need to rehash that.
thanks, poster above.

what the poster above didn't write is that it actually makes no difference at all that 'd' is the standard deviation in this problem. 'd' could be a completely random number and the problem would still work out the same way.
they're writing the problem with 'd' as the standard deviation for at least one, and probably both, of the following reasons: (a) to mess with your head, and (b) because IF 'd' IS the standard deviation, then the 68% and 16% take on a special significance (which is irrelevant here, but of tremendous importance in statistics).

but:

just think about SYMMETRY.

think of 'm' in the middle of a number line. then 'm + d' is just as far to the right of it as 'm - d' is to the left of it.

so:

(1) 68% of the stuff lies between m - d and m + d.
this means the other 32% (= 100% - 68%) of the stuff lies outside those boundaries.
because of the symmetry in the problem, this means that 16% of the stuff is to the left of m - d, and 16% of the stuff is to the right of m + d.
answer = 16%
sufficient

(2) by symmetry, the amount of stuff to the left of m - d must be the same as the amount of stuff to the right of m + d (because those two regions are mirror images of each other under the symmetry in the problem).
thus, answer = 16%
sufficient

answer = d