A machine is set to manufacture circular metal discs of diameter ; in fact, the diameter (in cm) of the discs it produces is a random variable with normal distribution having a mean of and a standard deviation of .
The demand of quality control place "acceptable limits between and ; all disks out of this range are rejected.
a) Given that a particular disk is accepted, find the probability that its diameter is more than .
b) It is decided that too many discs are rejected by the standard. If a new rejection rate is to be 10%, find the new acceptable limits, equally spaced on either side of the mean.
c) Use the fact that to estimate the mean area of the discs.