Question 1197346
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6. The time it takes for high school boys to run a mile is distributed 
normally with a mean of 460 seconds and a standard deviation of 40 seconds.(3 points)

a. What percentage of high school boys can run a mile in faster than 400 seconds?
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Both the solution and the answer in the post of @ewatrrr are incorrect.


The correct answer is   P = 0.0668.


Check yourself using the online calculator at this site

https://onlinestatbook.com/2/calculators/normal_dist.html


and you will  NEVER  make a mistake:  this calculator  PREVENTS  you of making mistakes.



Not only it prevents of making mistakes:  its plotting feature  EXPLAINS  you on the way,  what you are doing 

and what you should do.


Therefore,  this calculator is  INDISPESABLE  teaching/instructionasl tool,  when you learn this subject.


It works  BETTER  than any teacher.



In this problem,  they want you find the area under the normal curve  N(460,40)  on the left from the mark  x = 400.



Just the common sense tells you that the percentage of those who run faster than the mean value must be less than 50%.