2.
A machine is set to fill pots with yoghurt such that the mean weight of yoghurt in a pot is 505 grams.
To check that the machine is working properly, a random sample of 8 pots is selected. The weight of yoghurt, in grams, in each pot is as follows
$$\begin{array} { l l l l l l l l }
508 & 510 & 500 & 500 & 498 & 503 & 508 & 505
\end{array}$$
Given that the weights of the yoghurt delivered by the machine follow a normal distribution with standard deviation 5.4 grams,
- find a \(95 \%\) confidence interval for the mean weight, \(\mu\) grams, of yoghurt in a pot. Give your answers to 2 decimal places.