Each of a random sample of 50 one-pound coins was weighed and their masses, x grams, are summarised by 474,51, . - 4503.8276.

(a) Use an unbiased estimate of variance to calculate an approximate 90% confidence interval for the mean mass (in grams) of all one-pound coins, giving the end-values of the interval to two decimal places.

(b) Estimate the size of a random sample of one-pound coins that would be required to give a 95% confidence interval whose width is half that of the interval calculated in (a).

(c) It was found later that the scales were consistently underweighing by 0.05 grams. State which of the results of

(a) and

(b) should be amended and which should not. Give the amended values. (C)