4
The waiting time at a hospital's A\&E department may be modelled by a normal distribution with mean \(\mu\) and standard deviation \(\frac { \mu } { 2 }\).
The department's manager wishes a \(95 \%\) confidence interval for \(\mu\) to be constructed such that it has a width of at most \(0.2 \mu\).
Calculate, to the nearest 10, an estimate of the minimum sample size necessary in order to achieve the manager's wish.
(5 marks)
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