Machine components are mass-produced at a factory. A customer requires that the components should be 5.2 cm long but they will be acceptable if they are within limits 5.195 cm to 5.205 cm. The customer tests the components and finds that 10.75% of those supplied are over-size and 4.95% are under-size. Find the mean and standard deviation of the lengths of the components supplied, assuming that they are normally distributed. If three of the components are selected at random what is the probability that one is under-size, one is over-size and one satisfactory?