16 A survey of 120 adults found that the volume, \(X\) litres per person, of carbonated drinks they consumed in a week had the following results:
$$\sum x = 165.6 \quad \sum x ^ { 2 } = 261.8$$
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- Calculate the mean of \(X\).
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- (ii) Calculate the standard deviation of \(X\).
16 - Assuming that \(X\) can be modelled by a normal distribution find
16 - \(\mathrm { P } ( 0.5 < X < 1.5 )\)
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- (ii) \(\mathrm { P } ( X = 1 )\)
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- Determine with a reason, whether a normal distribution is suitable to model this data. [2 marks]
16 - It is known that the volume, \(Y\) litres per person, of energy drinks consumed in a week may be modelled by a normal distribution with standard deviation 0.21
Given that \(\mathrm { P } ( Y > 0.75 ) = 0.10\), find the value of \(\mu\), correct to three significant figures. [4 marks]