 ## (Solution document) A machine cuts plastic into sheets that are 30 feet (360 inches) long. Assume that the population of lengths is normally distributed. Complete parts...

A machine cuts plastic into sheets that are 30 feet ?(360 ?inches) long. Assume that the population of lengths is normally distributed. Complete parts? (a) and? (b).

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

n=________

(Round up to the nearest whole number as? needed.)

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

n=______

?(Round up to the nearest whole number as? needed.)

Which error tolerance requires a larger sample? size? Explain.

A.The tolerance E=0.125 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.

B.The tolerance E=0.0625 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.

C.The tolerance E=0.125 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy.

D.The tolerance E=0.0625 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy.