Fitting plungers into holes A random variable X has a N(u,, o?) distribution. Independently, a random variable Y has a N (Hy, o) distribution. What is the distribution of X -Y? In the manufacture of a certain mass-produced article, a circular plunger has to be fitted inside a circular cylinder. It is known that the manufacturing process is adjusted so that the diameters of plunger and cylinder are normally distributed, with mean and standard deviation as follows: External diameter of plunger: mean 99-7 mm, standard deviation 0-15 mm. Internal diameter of cylinder: mean 100-2 mm, standard deviation 0-20 mm. If components are selected at random for assembly, what proportion of plungers will not fit?

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