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?
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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Statistics and Probability
![Fitting plungers into holes
A random variable X has a N(µ,, 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F823623bd-2dc2-416d-aaca-55607fdf9c03%2F19e4be3b-a2f8-4c0d-97bf-1649068dbaa2%2Fzo8ng5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Fitting plungers into holes
A random variable X has a N(µ,, 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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