6. A computer company repairs large numbers of PCs and wants to estimate the mean time to repair a particular fault. Five repairs are chosen at random from the company's records and the times taken, in seconds, are
$$\begin{array} { l l l l l }
205 & 310 & 405 & 195 & 320
\end{array} .$$
- Calculate unbiased estimates of the mean and the variance of the population of repair times from which this sample has been taken.
It is known from previous results that the standard deviation of the repair time for this fault is 100 seconds. The company manager wants to ensure that there is a probability of at least 0.95 that the estimate of the population mean lies within 20 seconds of its true value.
- Find the minimum sample size required.
(Total 10 marks)