it is found that the standard deviation of the diameters of rivets produced by a certain machine over a long period of time is 0.018 cm.

it is found that the standard deviation of the diameters of rivets produced by a certain machine over a long period of time is 0.018 cm. The diameters of a random sample of 100 rivets produced by this machine in a day have a mean value of 0.476 cm. If the machine produces 2500 rivets a day, determine (a) the 90% confidence limits, and (b) the 95% confidence limits for an estimate of the mean diameter of all the rivets produced by the machine in a day