The engineering staff for the Bentim Manufacturing Company is considering sampling 30 bolts produced by a supplier for the company to determine the average diameter.The population is 200 bolts, the population standard deviation is known to be 0.015 inches,and the output measures are normally distributed.

a) Determine the standard error of the sampling distribution

b)The staff is troubled by bolts that do not fit the parts Bentrim is producing.Therefore,they wish to develop a method of determining when the bolts are too narrow or broad to fit the parts they are producing.If the mean diameter of bolt population is 0.75 inches,determine the largest average diameter a sample of 30 bolts should produce.

c)The staff has concluded that if the average they calculate from their sample is larger that the 95th percentile of the average bolts width,they will return the shipment of bolts and seek another supplier of bolts.What will be the minimum average width that will cause Bentrim to return the shipment?