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 be0.0003gram.

(a) The weight is weighed FIVE times. The mean result is10.0044grams. 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 of0.0001 with 98% confidence? Your answer must be a whole number.