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anonymous

  • one year ago

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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  1. phi
    • one year ago
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    change the pounds of force to # of std deviations above or below the mean.

  2. anonymous
    • one year ago
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    ? what i dont get what ur saying

  3. phi
    • one year ago
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    200 is the mean (the average) and the standard deviation is 3

  4. anonymous
    • one year ago
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    so make it 3lbs = standard deviation 200

  5. phi
    • one year ago
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    so what is 194 ? it is two standard deviations below the mean (i.e. 200 - 2*3)

  6. anonymous
    • one year ago
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    its 194 and 206

  7. phi
    • one year ago
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    yes, and 194 is 2 std dev below the mean what is 206 ?

  8. anonymous
    • one year ago
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    above the mean is 206

  9. anonymous
    • one year ago
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    so B is the one thats not true

  10. phi
    • one year ago
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    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 ?

  11. anonymous
    • one year ago
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    itll be 2 going up cause the standard deviation is 3

  12. phi
    • one year ago
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    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.

  13. phi
    • one year ago
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    |dw:1442259387016:dw|

  14. phi
    • one year ago
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    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 ?

  15. anonymous
    • one year ago
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    500 is half of 1000

  16. phi
    • one year ago
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    About 500 springs could withstand 200 lbs or more of force. is true.

  17. anonymous
    • one year ago
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    so that cant be the answer were looking for which is not true

  18. phi
    • one year ago
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    let's look at choice B About 950 springs could withstand between 194 and 206 lbs of force.

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  19. anonymous
    • one year ago
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    should i find half of 950

  20. anonymous
    • one year ago
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    half of 950 is 475

  21. phi
    • one year ago
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    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?

  22. phi
    • one year ago
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    so to check 950 are between -2 and +2 standard deviations what is 95% of 1000 ?

  23. anonymous
    • one year ago
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    yea and its still enough to with stand it

  24. phi
    • one year ago
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    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 ?

  25. anonymous
    • one year ago
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    would i do 1000/.95

  26. anonymous
    • one year ago
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    its 950

  27. phi
    • one year ago
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    95 % of 1000 means 0.95 * 1000 you get 950 (notice if you write 950/1000 and simplify you get 0.95 = 95%)

  28. phi
    • one year ago
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    in other words, choice B is correct 95% (of the 1000 springs) are between -2 and +2

  29. anonymous
    • one year ago
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    so choice B and C are correct so cross those out

  30. phi
    • one year ago
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    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|

  31. phi
    • one year ago
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    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 ?

  32. anonymous
    • one year ago
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    25

  33. anonymous
    • one year ago
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    no

  34. anonymous
    • one year ago
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    answer is D thanks

  35. phi
    • one year ago
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    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.

  36. anonymous
    • one year ago
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    so the answer i should choose is D

  37. phi
    • one year ago
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    no, the answer is not D. read what I posted up above.

  38. anonymous
    • one year ago
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    oh i see it so its A

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