Question

4 . A machine makes spherical balls. Diameters X are normally distributed with mean 240.0 mm and standard deviation 3.0 mm. Another machine, working independently, makes sockets with diameters Y that are normally distributed with mean 249.0 mm and standard deviation 4.0 mm. A ball will fit into the socket only if ; otherwise the ball is too big for the socket. Define the “gap” to be the difference between the socket diameter and the ball diameter. Therefore a ball fits the socket only if the gap is positive.

the mean gap is: 9

the standard deviation of the gap is: 5

a) A single ball is selected and has diameter 243.0 mm. If 3 sockets are selected at random, what is the probability that all three of them have diameters large enough to fit this ball?

Answer 1