6.36 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 is known to be 0.0002 gram.

1. (a) The weight is measured six times. The mean result is 10.0023 grams. Give a 99% confidence interval for the mean of repeated measurements of the weight.

2. (b) Based on the interval in part (a), do you think the scale is accurate? Explain your answer.

3. (c) How many measurements must be averaged to get a margin of error of ±0.0001 with 99% confidence?