The lengths of bolts produced by a manufacturer are assumed to be normally distributed with mean 9.0 cm and standard deviation 0.3 cm. (a) If a bolt is selected at random calculate the probability that it is: (i) less than 3.8 cm long; (ii) more than 9.1 cm long; (iii) between 3.85 cm and 9.05 cm long. Give all your answers to three decimal places. Cb) Calculate the length L, to two decimal places, such that 95% of all bolts manufactured are at least length L