An electric scale gives a reading equal to the true weight plus a random error that is normally distributed with mean 0 and standard deviation = .1 mg. Suppose that the results of five successive weighings of the same object are as follows: 3.142, 3.163, 3.155, 3.150, 3.141.

(a) Determine a 95 percent confidence interval estimate of the true weight.

(b) Determine a 99 percent confidence interval estimate of the true weight.