A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of a laboratory scale, that weight is weighed repeatedly. The scale readings are normally distributed with unknown mean. The population standard deviation of the scale readings is known to be 0.0003 gram. (a) The weight is weighed FIVE times. The mean result is 10.0044 grams. Give a 98% confidence interval for the mean weight. Please keep 5 decimals in your answer.
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(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence? Your answer must be a whole number.