anonymous
  • anonymous
The average pulling force that a sample of 1000 springs could take and still be able to spring back was 200 lbs with a standard deviation of 3 lbs. If the distribution follows a normal curve, which of the following is NOT true? About 15 springs could withstand less than 194 lbs of force About 950 springs could withstand between 194 and 206 lbs of force. About 500 springs could withstand 200 lbs or more of force. About 25 springs could withstand more than 206 lbs of force.
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  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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phi
  • phi
change the pounds of force to # of std deviations above or below the mean.
anonymous
  • anonymous
? what i dont get what ur saying
phi
  • phi
200 is the mean (the average) and the standard deviation is 3

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More answers

anonymous
  • anonymous
so make it 3lbs = standard deviation 200
phi
  • phi
so what is 194 ? it is two standard deviations below the mean (i.e. 200 - 2*3)
anonymous
  • anonymous
its 194 and 206
phi
  • phi
yes, and 194 is 2 std dev below the mean what is 206 ?
anonymous
  • anonymous
above the mean is 206
anonymous
  • anonymous
so B is the one thats not true
phi
  • phi
yes 206 is above (i.e. bigger than) 200 but by how much ? by 6 lbs but what is 6 lbs in standard deviations? i.e. how many std dev is 6 ?
anonymous
  • anonymous
itll be 2 going up cause the standard deviation is 3
phi
  • phi
yes, 206 is 2 std dev above the mean so lets look at the choices. this is the easiest one to figure out About 500 springs could withstand 200 lbs or more of force.
phi
  • phi
|dw:1442259387016:dw|
phi
  • phi
if the whole "bell curve" is 1000 springs and 1/2 of them are "above the mean" (i.e stronger than 200 lbs) how many is that ? in other words, what is 1/2 of 1000 ?
anonymous
  • anonymous
500 is half of 1000
phi
  • phi
About 500 springs could withstand 200 lbs or more of force. is true.
anonymous
  • anonymous
so that cant be the answer were looking for which is not true
phi
  • phi
let's look at choice B About 950 springs could withstand between 194 and 206 lbs of force.
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anonymous
  • anonymous
should i find half of 950
anonymous
  • anonymous
half of 950 is 475
phi
  • phi
choice B is saying 950 are between -2 and +2 standard deviations according to the bell curve posted up above, do you see 95% should be between -2 and +2?
phi
  • phi
so to check 950 are between -2 and +2 standard deviations what is 95% of 1000 ?
anonymous
  • anonymous
yea and its still enough to with stand it
phi
  • phi
in case it's not obvious, we have 1000 springs and we measure how strong they are and sort them by strength. If we do that, 95% of them will be between -2 and +2 std dev of the mean. what is 95% of 1000 ?
anonymous
  • anonymous
would i do 1000/.95
anonymous
  • anonymous
its 950
phi
  • phi
95 % of 1000 means 0.95 * 1000 you get 950 (notice if you write 950/1000 and simplify you get 0.95 = 95%)
phi
  • phi
in other words, choice B is correct 95% (of the 1000 springs) are between -2 and +2
anonymous
  • anonymous
so choice B and C are correct so cross those out
phi
  • phi
now let's look at About 25 springs could withstand more than 206 lbs of force. more than 206 means more than +2 std dev|dw:1442260036131:dw|
phi
  • phi
do you see springs stronger than 206 are in the right region above +2 that region is 2.5% of the 1000 what is 2.5% of 1000 ?
anonymous
  • anonymous
25
anonymous
  • anonymous
no
anonymous
  • anonymous
answer is D thanks
phi
  • phi
you could use a calculator. but 2.5% of 1000 is 0.025*100 = 25 so D is correct so by process of elimination A is wrong but if we look at choice A About 15 springs could withstand less than 194 lbs of force the number of springs less than -2 std dev should be 2.5% of 1000 (which we know is 25) 15 is too small, it should be 25 so that shows choice A is wrong.
anonymous
  • anonymous
so the answer i should choose is D
phi
  • phi
no, the answer is not D. read what I posted up above.
anonymous
  • anonymous
oh i see it so its A

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