13 In the South West region of England, 100 households were randomly selected and, for each household, the weekly expenditure, \(\pounds X\), per person on food and drink was recorded.
The maximum amount recorded was \(\pounds 40.48\) and the minimum amount recorded was £22.00
The results are summarised below, where \(\bar { X }\) denotes the sample mean.
$$\sum x = 3046.14 \quad \sum ( x - \bar { x } ) ^ { 2 } = 1746.29$$
13
- Find the mean of \(X\)
Find the standard deviation of \(X\)
[0pt]
[2 marks]
13
- (ii) Using your results from part (a)(i) and other information given, explain why the normal distribution can be used to model \(X\).
[0pt]
[2 marks]
13 - (iii) Find the probability that a household in the South West spends less than \(\pounds 25.00\) on food and drink per person per week.
13 - For households in the North West of England, the weekly expenditure, \(\pounds Y\), per person on food and drink can be modelled by a normal distribution with mean \(\pounds 29.55\)
It is known that \(\mathrm { P } ( Y < 30 ) = 0.55\)
Find the standard deviation of \(Y\), giving your answer to one decimal place.
[0pt]
[3 marks]