The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with a standard deviation of 0.3 minute. Find the percentage of a runners that will run the mile in less than 4 minutes?
A. 45.22%

B. 15.87%

C. 7.15%

D. 4.75%

Question

The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with a standard deviation of 0.3 minute. Find the percentage of a runners that will run the mile in less than 4 minutes? 
 A. 45.22%  
 
 B. 15.87%  
 
 C. 7.15%  
 
 D. 4.75%

anonymous · Answer

Considering that the time requirement is just within 2-standard deviations, and 1-stdev covers 68%, 2-stdev covers 95% and 3 stdev covers 99.8%, which answer seems reasonable?  This is why I hate multiple-guess tests as an instructor ;)

anonymous · Answer

hmm , not sure i dont get this at all /:

anonymous · Answer

Do you understand what a standard deviation is?

anonymous · Answer

no? i dont get this type of math

anonymous · Answer

This is a Statistics class right?

anonymous · Answer

no , its actually general math for High school online

anonymous · Answer

WOW.  Interesting.  Ok.

The standard deviation of a set is the essentially a measure of how close to average everyone is.  The smaller the standard deviation, the closer everyone is to the mean (or average).  If you were to plot these runner's times, you would notice that the graph is in the shape of a bell (hence the name Bell Curve).  With me so far?

anonymous · Answer

yes i understand , now what do i di next?

anonymous · Answer

Alright.  There are a couple of things to notice about Standard Deviations.  First, there is a relationship between the amount of data (runners in this case) and stdev's.  The first standard deviation will cover about 68% of the data (34% on either side of the average).  In your case, 68% of the runners will have times of 4.5 +/- 0.3 min.  Does that make sense?

anonymous · Answer

yes, so the answer would be A?

anonymous · Answer

Careful.  Your question wants under 4 minutes, and with your standard deviation width, that's closer to 2 stdevs.  2 standard deviations cover about 95% of the data (or approx. 47.5% either side of the mean).  What you're looking for is just UNDER 2 standard deviations.  Sorry I'm being so long about this, but I don't have my Stats book, and it's been awhile.

anonymous · Answer

If 5% of the runners are under 3.9 minutes (4.5 - 2standard deviations), a LITTLE more than that are under 4 minutes

anonymous · Answer

it would be D? & no problem

anonymous · Answer

If it's under 2-standard deviations, then it covers a little less than 95% of the data.  Which means a little MORE than 5% is left.  The answer is C.

anonymous · Answer

okat thanks (: