1. ## Normal Distribution Question

The cross-sectional area of plastic tubing for use in pulmonary resuscitators is normally distributed with mean = 12.5 mm^2 and standard deviation = 0.2 mm^2. When the area is less than 12.0 mm^2 or greater than 13.0 mm^2, the tube does not fit properly. If the tubes are shipped in boxes of 1000, how many wrong-sized tubes per box can doctors expect to find?

I get that I just find the probability and then I can know how many tubes out of 1000 are wrong. 12 and 13 are each 2.5 standard deviations away from the mean... So do I just find the probability between -2.5 and 2.5 standard deviations and then take 1 - the answer?

2. Originally Posted by Janu42
The cross-sectional area of plastic tubing for use in pulmonary resuscitators is normally distributed with mean = 12.5 mm^2 and standard deviation = 0.2 mm^2. When the area is less than 12.0 mm^2 or greater than 13.0 mm^2, the tube does not fit properly. If the tubes are shipped in boxes of 1000, how many wrong-sized tubes per box can doctors expect to find?

I get that I just find the probability and then I can know how many tubes out of 1000 are wrong. 12 and 13 are each 2.5 standard deviations away from the mean... So do I just find the probability between -2.5 and 2.5 standard deviations and then take 1 - the answer?
Sounds like you are on the right track, try this..

$1000\times 2P(X<12) = 1000\times \left( 2\times P\left(Z<\frac{12-\mu}{\sigma}\right)\right)$