The time taken, in minutes, by Domesat to install a domestic satellite system may be modelled by a normal distribution with unknown mean, \(\mu\), and standard deviation 15 .
The times taken, in minutes, for a random sample of 10 installations are as follows.
\(\begin{array} { l l l l l l l l l l } 47 & 39 & 25 & 51 & 47 & 36 & 63 & 41 & 78 & 43 \end{array}\)
Construct a \(98 \%\) confidence interval for \(\mu\).
The time taken, \(Y\) minutes, by Teleair to erect a TV aerial and then connect it to a TV is known to have a mean of 108 and a standard deviation of 28.
Estimate the probability that the mean of a random sample of 40 observations of \(Y\) is more than 120 .
Indicate, with a reason, where, if at all, in this question you made use of the Central Limit Theorem.
(2 marks)