4 The error, \(X ^ { \circ } \mathrm { C }\), made in measuring a patient's temperature at a local doctors' surgery may be modelled by a normal distribution with mean \(\mu\) and standard deviation \(\sigma\). The errors, \(x ^ { \circ } \mathrm { C }\), made in measuring the temperature of each of a random sample of 10 patients are summarised below. $$\sum x = 0.35 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 0.12705$$ Construct a \(99 \%\) confidence interval for \(\mu\), giving the limits to three decimal places.
(5 marks)