A machine cuts plastic into sheets that are 35 feet (420 inches) long. Assume that the population of lengths is normally distributed.

(a) The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a

90% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.

b)Repeat part (a) using an error tolerance of 0.0625 inch.

Which error tolerance requires a larger sample size? Explain