(A) Shafts manufactured for use in optical storage devices have diameters that are normally distributed with a mean of 0.652 cm and a standard deviation of 0.003 cm. The specification for the shaft diameter is 0.650 0.005 cm.

(1) What percentage of the shafts manufactured by this process meet the specifications

(2) The process mean can be adjusted through calibration. If the mean is set to 0.650 cm, what percentage of the shafts will meet the specification. (3) If the mean is set to 0.650 cm, what must the standard deviation be so that 99% of the shafts will meet specification

(B) A supplier sells synthetic fibres to a manufacturing company. A simple random sample of 81 fibres is selected from a shipment. The average breaking strength of the sample is 29 kg and the standard deviation is 9 kg.

(1) Find the 95% confidence interval for the mean breaking strength of all fibres in the shipment.

(2) How many fibres must be sampled so that a 99% confidence interval specifies the mean to within 1 kg.