2 The widths, \(w \mathrm {~cm}\), of a random sample of 150 leaves of a certain kind were measured. The sample mean of \(w\) was found to be 3.12 cm . Using this sample, an approximate \(95 \%\) confidence interval for the population mean of the widths in centimetres was found to be [3.01, 3.23].

1. Calculate an estimate of the population standard deviation.
2. Explain whether it was necessary to use the Central Limit theorem in your answer to part (a). [1]