7.106 Accuracy of a laboratory scale. To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings in the past has been 0.0013 gram.
(a) The weight is measured five times. The mean result is 10.0009 grams. Give a 98% confidence interval for the mean of repeated measurements of the weight.
(b) How many measurements must be averaged to get an expected margin of error no more than 0.001 with 98% confidence?