6 The daily takings, \(
) x\(, for a shop were noted on 30 randomly chosen days. The takings are summarised by \)\Sigma x = 31500 , \Sigma x ^ { 2 } = 33141816$.
- Calculate unbiased estimates of the population mean and variance of the shop's daily takings.
- Calculate a \(98 \%\) confidence interval for the mean daily takings.
The mean daily takings for a random sample of \(n\) days is found.
- Estimate the value of \(n\) for which it is approximately \(95 \%\) certain that the sample mean does not differ from the population mean by more than \(
) 6$.