4 The mean mass of packets of sugar is supposed to be 505 g . A random sample of 10 packets filled by a certain machine was taken and the masses, in grams, were found to be as follows.
$$\begin{array} { l l l l l l l l l l }
500 & 499 & 496 & 495 & 498 & 490 & 492 & 501 & 494 & 494
\end{array}$$
- Find unbiased estimates of the population mean and variance.
The mean mass of packets produced by this machine was found to be less than 505 g , so the machine was adjusted. Following the adjustment, the masses of a random sample of 150 packets from the machine were measured and the total mass was found to be 75660 g . - Given that the population standard deviation is 3.6 g , test at the \(2 \%\) significance level whether the machine is still producing packets with mean mass less than 505 g .
- Explain why the use of the normal distribution is justified in carrying out the test in part (ii). [1]