Math Help - Using the Normal Distribution as a Model for Individual Measurements

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?

Thanks!

z=(x-mean)/standard dev

so

z1=(13-12.5)/0.2

z2=(12-12.5)/0.2

look up z1 and z2 in the normal distribution tables.

Use these to find
P(x<z1)=P(x<13)
P(x<z2)=P(x<12)

Then P(x<13)-P(x<12) = P(12<x<13)

Multiply by 1000

Should work a treat.


-Do you get 68 wrong sized tubes?