The weight of a bag of sugar is normally distributed with mean of 500g and a standard deviation of 20g.

a) If a bag of sugar is randomly selected,

i. What is the probability that its weight is more than 510g?

ii. What is the probability that its weight is between 483g and 535g?

iii. If 20% of the bags are above a certain weight W, find the value of W.

b) A box contains 10 such bags of sugar. What is the probability that the mean weight is between 492g and 523g?