8.
A company has a customer services call centre. The company believes that the time taken to complete a call to the call centre may be modelled by a normal distribution with mean 16 minutes and standard deviation \(\sigma\) minutes.
Given that \(10 \%\) of the calls take longer than 22 minutes,
- show that, to 3 significant figures, the value of \(\sigma\) is 4.68
- Calculate the percentage of calls that take less than 13 minutes.
A supervisor in the call centre claims that the mean call time is less than 16 minutes. He collects data on his own call times.
- \(20 \%\) of the supervisor's calls take more than 17 minutes to complete.
- \(10 \%\) of the supervisor's calls take less than 8 minutes to complete.
Assuming that the time the supervisor takes to complete a call may be modelled by a normal distribution, - estimate the mean and the standard deviation of the time taken by the supervisor to complete a call.
- State, giving a reason, whether or not the calculations in part (c) support the supervisor's claim.
\section*{9.}
A fast food company has a scratchcard competition. It has ordered scratchcards for the competition and requested that \(45 \%\) of the scratchcards be winning scratchcards.
A random sample of 20 of the scratchcards is collected from each of 8 of the fast food company's stores.
Assuming that \(45 \%\) of the scratchcards are winning scratchcards, calculate the probability that in at least 2 of the 8 stores, 12 or more of the scratchcards are winning scratchcards.
[0pt]
[Total 5 marks]
END OF TEST