The Professor's Response

Hello Professor,

In the homework for chapter 5, number 40 asks "The fastest finishing times for the NY marathon are normally distributed with a mean of 147.08 minutes and a standard deviation of 1.48 minutes. Find the finishing time for the slowest 4% of winning NY marathon runners."

After viewing the answer, it seems that the bell curve was cut at the 4% on the right side of the curve. I'm still confused as to why we wouldn't cut it on the left side (making the z-score negative) since it is asking for the slowest 4%?

Thank you!

Sofia Novo

See the professor's answer below.

Hi Sofia,

Since this problem is looking at the slowest 4%, shouldn't those runners take longer than average to finish the race? In other words, if the average runner finishes in 147.08 minutes, the slow runners should take longer than that number. The numbers on the right side of the curve will be longer than average, so that is why our answer should be on the right side of the curve.

Another way to think of it is to say, "slow runners take longer to finish." If I said, "the longest 4% of finishing times," it should be clear that we are working on the right side. Longest finishing times are the times belonging to the slowest runners, so the slow runners are on the right.

Always compare your final answer to the mean to make sure it makes sense, and be extra cautious when the problem deals with time.

I hope that helps,

Professor McGuckian