1 A random variable has a normal distribution with unknown mean \(\mu\) and known standard deviation 0.19 . In order to estimate \(\mu\) a random sample of five observations of the random variable was taken. The values were as follows.
$$\begin{array} { l l l l l }
5.44 & 4.93 & 5.12 & 5.36 & 5.40
\end{array}$$
Using these five values, calculate,
- an estimate of \(\mu\),
- a 95\% confidence interval for \(\mu\).