Normal distribution 7) An assembly plant obtains a component from two manufacturers A and 3. Manufacturer A supplies 250 per day with diameter being a normally distrbuted random variable with mean 15.98 mm and standard deviation 0.2 mm. whilst B supplies 750 per day with diameter being a normally distributed random variable with mean 16.10 mm and standard deviation 0.16 mm. it is found that4 % of components from A are scratched and that 9 % of components from B are scratched. Components are unacceptable if scratched or with diameter outside the range (15.70 mm. 16.30 mm). a) What proportion is unacceptable? b) Suppose randomly chosen part is found to be unacceptable. What is the probability it was made by A? c) What is the probability of the diameter of two randomly picked components differing by more than 0.6 mm if (i) they both come from manufacturer A or (ii) one comes from manufacturer A and the other one from B