a machine cuts plastic into sheets that are 40 feet long Ass

a machine cuts plastic into sheets that are 40 feet long. Assumethat the population of lengths is normally distributed.

a. The company wants to estimate the mean length the machine iscutting the plastic within 0.125 inch. Determine the minimum samplesize required to construct a 90% confidence interval for thepopulation mean. Assume the population standard deviation is 0.25 inch.

n=_______ (round to the nearest whole number)

b. repeat part a using an error tolerance of 0.0625 inch.

n= ______( round up to the nearest whole number)

Which error tolerance requires a larger sample size Explain?

Solution

(a)Given a=1-0.9=0.1, Z(0.05) =1.645 (from standrad normal table)

So n=(Z*s/E)^2

=(1.645*0.25/0.125)^2

=10.8241

Take n=11

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(b)So n=(Z*s/E)^2

=(1.645*0.25/0.0625)^2

=43.2964

Take n=44

0.0625 error tolerance requires a larger sample size based on part b