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.

Question

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.

phi · Answer

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

anonymous · Answer

? what i dont get what ur saying

phi · Answer

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

anonymous · Answer

so make it 3lbs = standard deviation 200

phi · Answer

so what is 194 ?   it is two standard deviations below the mean  (i.e. 200 - 2*3)

anonymous · Answer

its 194 and 206

phi · Answer

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

anonymous · Answer

above the mean is 206

anonymous · Answer

so B is the one thats not true

phi · Answer

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 · Answer

itll be 2 going up cause the standard deviation is 3

phi · Answer

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 · Answer

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