The weights, $$\(x \mathrm{~kg}\)$$, of each of 10 watermelons selected at random from Priya's shop were recorded. The results are summarised as follows $$\[ \sum x=114.2 \quad \sum x^{2}=1310.464 \]$$ Calculate a 95\% confidence interval for the mean weight of watermelons in Priya's shop. Give the limits of your confidence interval to 2 decimal places. (4) Priya claims that the confidence interval in part (b) suggests that nearly all of the watermelons in her shop weigh more than $$\(10.5 \mathrm{~kg}\)$$

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