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A machine cuts plastic into sheets that are 5|] 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 Iwithin 0.125 inch. Determine the minimum sample size required to constnict a 95% condence interval for the population mean. Assume the population standard deviation is 0.25 inch. n: Round up to the nearest whole number as needed.) to} Repeat part (at using an error tolerance of 0.0625 inch. FD (Round up to the nearest whole number as needed.) Which error tolerance requires a larger sample size? Explain. O A. 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 accu racy. O 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. 0 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. 0 D. The tolerance E = D. 125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy