3. The weight of a large loaf bread is normally distributed with mean 420g and standard deviation 30g. Assume the weights of different loaves are independent. (a) Find the probability that a randomly selected large loaf bread weighs more than 435g. (b) Ten large loaves are randomly selected. Find the probability that 5 of them each weigh more than 435g. (c) One hundred large loaves are randomly selected. Using the Central Limit Theorem (normal approximation to the binomial), find the approximate probability that i. at least 30 loaves each weigh more than 435g. ii. between 20 and 30 (inclusive) loaves each weigh more than 435g. (d) The weight of a small loaf of bread is normally distributed with mean 220g and standard deviation 10g. Find the probability that the total weight of 5 large loaves and 10 small loaves lies between 4.25kg (4250g) and 4.4kg (4400g)