<PRE><B>Question 360241</B>
In this case, we only need to find the running time that corresponds with the LOWER 25% z-score (since the lower times are the better times)!  Tricky, tricky! &lt;br&gt;

Remember, the z-score is simply (x-xbar)/s where xbar is the mean, x is our value of interest, and s is the standard deviation.&lt;br&gt;

So first we need to find the z-score that corresponds with the lower 25% value.  We can do this in several ways, by consulting z-score tables or z-score calculators.&lt;br&gt;

My z-score calculator tells me we are looking for the z-score of about -0.67 to capture 25% of values to the left and 75% of values to the right.&lt;br&gt;

Then we just need to convert this z-score back into a running time, like this:&lt;br&gt;

{{{(x-45.8)/3.6=-0.67}}}&lt;br&gt;

{{{(x-45.8)=-0.67*3.6}}}&lt;br&gt;

{{{(x-45.8)=-2.412}}}&lt;br&gt;

{{{x=45.8-2.412}}}&lt;br&gt;

{{{x=43.388}}}&lt;br&gt;

Therefore our cutoff time should be about 43.388 minutes.&lt;br&gt;

Notice that even though 43.388 is less than the mean, it still reflects the point where the upper 25% of the values end.  This is kind of tricky, because usually the higher numbers are associated with the &quot;upper&quot; values.&lt;br&gt;

It should be immediately obvious that a runner who runs the course in 40 minutes (which is LESS than the 43.388 cutoff time) on the tryout run should qualify for the race!&lt;br&gt;

I hope this helps!&lt;br&gt;</PRE>