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.

- anonymous

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- phi

change the pounds of force to # of std deviations above or below the mean.

- anonymous

? what i dont get what ur saying

- phi

200 is the mean (the average)
and the standard deviation is 3

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- anonymous

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)

- anonymous

its 194 and 206

- phi

yes, and 194 is 2 std dev below the mean
what is 206 ?

- anonymous

above the mean is 206

- anonymous

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 ?

- anonymous

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 ?

- anonymous

500 is half of 1000

- phi

About 500 springs could withstand 200 lbs or more of force.
is true.

- anonymous

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.

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- anonymous

should i find half of 950

- anonymous

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 ?

- anonymous

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 ?

- anonymous

would i do 1000/.95

- anonymous

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

- anonymous

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 ?

- anonymous

25

- anonymous

no

- anonymous

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.

- anonymous

so the answer i should choose is D

- phi

no, the answer is not D. read what I posted up above.

- anonymous

oh i see it so its A

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