7. A machine produces metal containers. The weights of the containers are normally distributed. A random sample of 10 containers from the production line was weighed, to the nearest 0.1 kg , and gave the following results
$$\begin{array} { l l l l l }
49.7 , & 50.3 , & 51.0 , & 49.5 , & 49.9
50.1 , & 50.2 , & 50.0 , & 49.6 , & 49.7 .
\end{array}$$
- Find unbiased estimates of the mean and variance of the weights of the population of metal containers.
The machine is set to produce metal containers whose weights have a population standard deviation of 0.5 kg .
- Estimate the limits between which \(95 \%\) of the weights of metal containers lie.
- Determine the \(99 \%\) confidence interval for the mean weight of metal containers.