Question

In a factory which is producing chair, all chairs produced had different lengths on a given day because of machine error, then randomly packed and shipped to different places and people. We want to know the length of the longest chair produced that day. Create a good statistical estimator to address this problem and evaluate its properties.

Answer 1

>> We will take the samples of the chair randomly at least 50 samples.( For normal distribution assumption) and measure the length of the chair.  

>> let x1, x2 ........x50 be the length of the chai leg.

>> Then find the average of all 50 lengths. let it be X-bar

>> Find the standard error s of the length using sample

>> The length of the largest chair can be approximated by the upper limit of the length of the chai at 5% level of significance ( one can choose any level of significance and corresponding Z score )

>> length of largest leg is

{ X-bar + 1.96 x s / sqrt (n) }