A machine cuts plastic into sheets that are 50 feet ?(600 ?inches) long. Assume that the population of lengths is normally distributed. Complete parts? (a) and? (b).
?(a)The company wants to estimate the mean length the machine is cutting the plastic within 0.25 inch. Determine the minimum sample size required to construct a 90?% confidence interval for the population mean. Assume the population standard deviation is 0.50 inch.
?(b) Repeat part? (a) using an error tolerance of 0.125 inch.
Which error tolerance requires a larger sample? size? Explain.
A. The tolerance Eequals =0.125 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy.
B. The tolerance Eequals 0.125 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.
C. The tolerance Eequals =0.25 inch requires a larger sample size. As error size? increases, a larger sample must be taken to ensure the desired accuracy.
D. The tolerance Eequals =0.25 inch requires a larger sample size. As error size? decreases, a larger sample must be taken to ensure the desired accuracy