An estimate of the average length of pins produced by an automatic lathe is wanted to within 0.002 inch with a 95% confidence level. σ is guessed to be 0.015 inch.

a. What is the minimum sample size?

b. If the value of σ may be anywhere between 0.010 and 0.020 inch, tabulate the minimum sample size required for σ values from 0.010 to 0.020 inch.

c. If the cost of sampling and testing n pins is (25 + 6n) dollars, tabulate the costs for σ values from 0.010 to 0.020 inch.