Question

The weights of certain machine components are normally distributed with a mean of 8.45g and a standard deviation of 0.06g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve as limits used to identify which components should be rejected. Round to the nearest hundredth of a gram.

Answer 1

Here it is required to find the two weights that separate the top 3% and the bottom 3% of a normally distributed random variable, denoting the weights of certain machine components, with a mean of 8.4 g and standard deviation of 0.06g. It is equivalent to find the 2 points which 0.03^th quantile and 0.97^th quantile of a normally distributed random variable with a mean of 8.4 g and standard deviation of 0.06g. Using qnorm() routine in R software these 2 points are found to be 8.34 and 8.5.

Ans: That is 8.34g and 8.56g are the two weights that separate the top 3% and the bottom 3%.