elementary stats

a machine cuts plastic into sheets that are 50 feet (600 inches) long. Assume that the population of lenghts is normally distributed.

a. the company wants to estimate the mean lenght 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.
b. repeat part (a) using an error tolerance of 0.0625 inch. which error tolerance requires a larger sample size? explain

minimum sample size is given by:

\(\displaystyle n=\left(\frac{z\cdot \sigma}{E}\right)^{2}\)

Sub in the given info. The z-score for a 95% CI is 1.96.

You will get a non-integer solution. So, round up to the next integer.