6 A machine produces metal discs whose diameters have a normal distribution. The mean of this distribution is intended to be 10 cm . Accuracy is checked by measuring the diameters of a random sample of six discs. The diameters, in cm, are as follows. $$\begin{array} { l l l l l l } 10.03 & 10.02 & 9.98 & 10.06 & 10.08 & 10.01 \end{array}$$ Calculate a 99\% confidence interval for the mean diameter of all discs produced by the machine. Deduce a 99\% confidence interval for the mean circumference of all discs produced by the machine.