6. The time taken, in minutes, by children to complete a mathematical puzzle is assumed to be normally distributed with mean \(\mu\) and standard deviation \(\sigma\). The puzzle can be completed in less than 24 minutes by \(80 \%\) of the children. For \(5 \%\) of the children it takes more than 28 minutes to complete the puzzle.

1. Show this information on the Normal curve below.
2. Write down the percentage of children who take between 24 minutes and 28 minutes to complete the puzzle.
3. 1. Find two equations in \(\mu\) and \(\sigma\).
   2. Hence find, to 3 significant figures, the value of \(\mu\) and the value of \(\sigma\). A child is selected at random.
4. Find the probability that the child takes less than 12 minutes to complete the puzzle.
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