The empirical rule says that about 68% of any normal distribution lies within one standard deviation of the mean. This leaves 32% of the distribution that lies outside this range, with about 16% to either side.
At the 16th percentile, there is a value of
such that
where
is the standard deviation for the distribution, and
is the random variable corresponding to the standard normal distribution. This value of
would correspond roughly to a z-score of
.
You're told that
lies at the 15th percentile, so that
Roughly, then, it'd be fair to say that
. So you have
which falls between (A) and (B). To narrow down the choice, notice that
would have be slightly larger than 340 in order to have
. This brings
closer to the mean, and thus suggests the standard deviation for the distribution is actually smaller than our approximation.
This tells us that (A) is the answer.
