Morgan is investigating the body length, $$\(b\)$$ centimetres, of squirrels. A random sample of 8 squirrels is taken and the data for each squirrel is coded using $$\[ x=\frac{b-21}{2} \]$$ The results for the coded data are summarised below $$\[ \sum x=-1.2 \quad \sum x^{2}=5.1 \]$$ (a) Find the mean of $$\(b\)$$ (3) (b) Find the standard deviation of $$\(b\)$$ (3) A 9th squirrel is added to the sample. Given that for all 9 squirrels $$\(\sum x=0\)$$ (c) find (i) the body length of the 9th squirrel, (2) (ii) the standard deviation of $$\(x\)$$ for all 9 squirrels. (2)

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