Consider the following industrial process: large rectangular pieces of wood are

Question

Consider the following industrial process: large rectangular pieces of wood are inserted into a machine that will cut them along pre-drawn mines in order to obtain pieces of 150 cm each, In view of a minor defect of the machine, it almost never cuts the pieces of wood along the prescribed lines. Empirical evidence has shown that the absolute value of the error never exceeds 0.75 cm It is important for the industry to estimate the average error, mu, which is suffered by the machine when cutting the wood. Propose an estimator mu^hat_n of mu. Use a CLT approximation to determine the smallest sample size n for which the probability that mu^hat_n is within 0.2 cm of mu is at least equal to 0.95.

Explanation / Answer

from above as error is approximately uniformly distributed from 0 to 0.75 cm

1) hence estimate of average =(0+0.75)/2=0.375

2) std deviation =(b-a)/(12)1/2 =0.75/(12)1/2 =0.2165

for 95% CI, z=1.96

margin of error E =0.2 cm

hence sample size n=(z*std deviation/E)2 =~5

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