Moderate -0.8 This is a straightforward S1 question testing standard confidence interval and CLT application. Part (a) requires routine calculation of a confidence interval with known variance (formula provided in formula book), part (b) is a direct CLT application with standardization, and part (c) asks for simple identification of where CLT was used. All steps are mechanical with no problem-solving or conceptual insight required beyond basic recall.
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)
6
\begin{enumerate}[label=(\alph*)]
\item 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 $\mu$.
\item 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 .
\item Indicate, with a reason, where, if at all, in this question you made use of the Central Limit Theorem.\\
(2 marks)
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\hfill \mbox{\textit{AQA S1 2009 Q6 [11]}}