The National Institute of Standards and Technology (NIST) supplies standard materials whose physical properties are supposed to be known. For example, you can buy from NIST a copper sample whose melting point is certified to be 1084.80. Of course, no measurement is exactly correct. NIST knows the variability of its measurements very well, so it is quite realistic to assume that the population of all measurements of the same sample has the Normal distribution with mean equal to the true melting point and standard deviation = 0.25C. Here are six measurements on the same copper sample, which is supposed to have melting point 1084.80.

1084.55 1084.89 1085.02 1084.79 1084.69 1084.86

NIST wants to give the buyer of this sample a 70.5 % confidence interval for its true melting point. What is this interval? Follow the four-step process.