A process that manufactures piston rings produces rings whose diameters (in centimeters) vary according to the probability density function
a. Find the mean diameter of rings manufactured by this process.
b. Find the standard deviation of the diameters of rings manufactured by this process.
c. Find the cumulative distribution function of piston ring diameters.
d. What proportion of piston rings have diameters less than 9.75 cm?
e. What proportion of piston rings have diameters between 9.75 and 10.25 cm?
(d) None of them. F(9.75) = 0.
(e) All of them. F(10.25) = 1, so all of the rings have diameters less than or equal to 10.25 cm. Since none of the rings have diameters less than 9.75 cm, all of them have diameters between 9.75 and 10.25 cm.
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