Statement 1
the z-score of 194 lbs is
![\frac{194-200}{3} =-2](https://tex.z-dn.net/?f=%20%5Cfrac%7B194-200%7D%7B3%7D%20%3D-2)
Reading the probability for z-score -2 on the table
![1-P(Z\ \textless \ 2)=1-0.9772=0.0228](https://tex.z-dn.net/?f=1-P%28Z%5C%20%5Ctextless%20%5C%202%29%3D1-0.9772%3D0.0228)
Then 0.0228×1000=23 spring that could withstand less than 194 lbs of force
Statement 2
The z-score of 194 lbs is -2
The z-score of 206 is
The probability between -2 and 2 is given by
![P(Z\ \textless \ 2)-P(Z\ \textless \ -2)](https://tex.z-dn.net/?f=P%28Z%5C%20%5Ctextless%20%5C%202%29-P%28Z%5C%20%5Ctextless%20%5C%20-2%29)
![P(Z\ \textless \ 2)-(1-P(Z\ \textless \ 2)=0.9772-0.0228=0.9544](https://tex.z-dn.net/?f=P%28Z%5C%20%5Ctextless%20%5C%202%29-%281-P%28Z%5C%20%5Ctextless%20%5C%202%29%3D0.9772-0.0228%3D0.9544)
Then 0.9544×1000=954.4 springs could withstand the force between 194 lbs and 206 lbs
Statement 3
The z-score for 200lbs is 0, as it is the mean. The area to the right of z=0 is 0.5 which means half of 1000 springs could withstand the force more than 200lbs
Statement 4
The z-score of 206lbs is 2
The value of
![P(Z\ \textgreater \ 2)=1-P(Z\ \textless \ 2)=1-0.9772=0.0228](https://tex.z-dn.net/?f=P%28Z%5C%20%5Ctextgreater%20%5C%202%29%3D1-P%28Z%5C%20%5Ctextless%20%5C%202%29%3D1-0.9772%3D0.0228)
Which is 0.0228×1000=22.8 springs could withstand more than 200 lbs of force
So the statement 1 is incorrect