Question 1197346: 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?
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
µ = 460 and σ = 40
What percentage of high school boys can run a mile in faster than 400 seconds?
P(x> 400) = 1 - P( x ≤ 400) = 1 - normalcdf(smaller, larger, µ, σ)
P(x> 400)= 1 -normalcdf(-9999, 400, 450, 40) = 1 - .0668 = .9332
-9999 being a place holder for the smaller number
NOte: σ = 40, 400 is 1.5sd below mean.
What percentage of high school boys can run a mile in faster than 400 seconds?
93.32%
Wish You the Best in your Studies.
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
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%.
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