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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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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  • phi
change the pounds of force to # of std deviations above or below the mean.
? what i dont get what ur saying
  • phi
200 is the mean (the average) and the standard deviation is 3

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Other answers:

so make it 3lbs = standard deviation 200
  • phi
so what is 194 ? it is two standard deviations below the mean (i.e. 200 - 2*3)
its 194 and 206
  • phi
yes, and 194 is 2 std dev below the mean what is 206 ?
above the mean is 206
so B is the one thats not true
  • 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 ?
itll be 2 going up cause the standard deviation is 3
  • 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
|dw:1442259387016:dw|
  • 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 ?
500 is half of 1000
  • phi
About 500 springs could withstand 200 lbs or more of force. is true.
so that cant be the answer were looking for which is not true
  • phi
let's look at choice B About 950 springs could withstand between 194 and 206 lbs of force.
1 Attachment
should i find half of 950
half of 950 is 475
  • 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
so to check 950 are between -2 and +2 standard deviations what is 95% of 1000 ?
yea and its still enough to with stand it
  • 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 ?
would i do 1000/.95
its 950
  • 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
in other words, choice B is correct 95% (of the 1000 springs) are between -2 and +2
so choice B and C are correct so cross those out
  • 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
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 ?
25
no
answer is D thanks
  • 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.
so the answer i should choose is D
  • phi
no, the answer is not D. read what I posted up above.
oh i see it so its A

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