A painter built a ladder using 18 rungs. The rungs on the ladder were 5.7 inches apart and 1.1 inches thick. What is the distanc
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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.
At the 16th percentile, there is a value of
where
You're told that
Roughly, then, it'd be fair to say that
which falls between (A) and (B). To narrow down the choice, notice that
This tells us that (A) is the answer.