2. A manufacturer produces bolts which are claimed to have core diameter 6.0mm. (a) A sample of 24 bolts is selected and the diameters measured to the nearest 0.01 mm. The results are: 5.98 5.97 5.96 5.92 5.90 5.82 5.96 5.95 6.00 5.82 5.99 5.94 6.02 5.93 5.84 6.07 5.96 5.85 5.87 5.95 5.91 5.86 5.91 5.85 Use Excel to calculate the mean and standard deviation of this sample and comment very briefly on the results in the context of the question. (b) In reality the bolts are normally distributed with a mean diameter of 5.9mm and a standard deviation of 0.08mm. If the diameter is less than 5.7mm the bolts are liable to become loose, so they are not usable. Use Excel to calculate the probability that a bolt is unusable for this reason? It is found that if the diameter is greater than 6.05mm the bolt is difficult to insert. Use Excel to calculate the probability that a bolt will lie in the useful operational range with a diameter between 5.7mm and 6.05mm