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### Regional Marathon Problem

```
Date: 9 Jan 1995 15:55:51 -0500
From: Lori Yoshida
Subject: (none)

Those wanting to participate in a state marathon race must first qualify
by running in a regional marathon.  The times of the 3750 regional runners
are normally distributed with a mean of 198 min 36 s and a standard
deviation of 23 min 14 s.  If there are to be only 600 runners in the state
marathon, what is the slowest time that will qualify a regional runner
for the state race?
```

```
Date: 19 Jan 1995 20:22:13 GMT
From: Dr. Math
Subject: Re: (none)

Hey,

Well I'm not sure how much you know about Normal distributions.
Probably the easiest way to work with these is to use a normal
distribution table. (That is what I did.)  Once you have a normal
distribution table, it gives you the percentage of the results that are
within  a certain deviation of the mean.  Well 600 is .16 of the total
entries, so that means that .34 of the participants are between that
cut-off time and the mean.  So now we look at the table and see that
that is one standard deviation from the mean.  Now we subtract the
standard deviation from the mean time and find that the time needed
to qualify is 164 min and 22 secs.  Hope that makes some sense.
I'm not sure what your background is in this and mine is pretty
limited so I know that this explanation is limited.

Well, good luck.
Ethan Doctor On Call
```
Associated Topics:
High School Statistics

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