Regional Marathon ProblemDate: 9 Jan 1995 15:55:51 -0500 From: Lori Yoshida Subject: (none) Please help me with the following problem: 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 |
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