2. Data relating to the lifetimes (to the nearest hour) of a random sample of 200 light bulbs from the production line of a manufacturer were summarised in a grouped frequency table. The mid-point of each class in the table was represented by \(x\) and the corresponding frequency for that class by \(f\). The data were then coded using: $$y = \frac { ( x - 755.0 ) } { 2.5 }$$ and summarised as follows: $$\sum f y = - 467 , \sum f y ^ { 2 } = 9179$$ Calculate estimates of the mean and the standard deviation of the lifetimes of this sample of bulbs.
(4 marks)
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