the means of the O.D. of the rods and the I.D. of the tubes are 2.5 sd apart
the two normal bell curves intersect midway between the means
... 1.25 s.d. above the rod O.D. and 1.25 s.d. below the tube I.D.
the tubes below this intersection are too small for the corresponding rods
the rods above this intersection are too big for the corresponding tubes
find the areas under the "non-fitting" sections to find the probability
... fraction of rods above 1.25 s.d. AND fraction of tubes below 1.25 s.d.
A factory makes steel rods and steel tubes. The diameter of a steel rod is normally distributed with mean 3.55cm and standard deviation 0.02cm. The internal diameter of a steel tube is normally distributed with mean 3.60cm and standard deviation 0.02cm. A rod and a tube are selected at random. Find the probability that the rod cannot pass through the tube.
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