A credit card company wants to determine the mean income of its card holders. A random sample of 225 card holders was dr

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A credit card company wants to determine the mean income of its
card holders. A random sample of 225 card holders was drawn and the
sample average income was £16 450 with a standard deviation of
£3675.
(a) Construct a 99% confidence interval for the true mean
income.
(b) Management decided that the confidence interval in (a) was
too large to be useful. In particular, the management wanted to
estimate the mean income to within £200, with a confidence level of
99%. How large a sample should be selected?