The mass of packs of a certain type of coffee is normally distributed with a mean of 500 g and a standard deviation of 1.5 g.

(a) Find the probability that a pack weighs more than 520g

(b) The lightest 4% of the packs weigh less than a, while the heaviest 4% of the packs weigh more than b. Find a and b.

The packs in question (b) are rejected from the market.

(c) In a daily production of 1600 packs how many of them are expected to be rejected?

(d) We select 2 packs. Find the probability that both are rejected.

(e) We select 5 packs. Find the probability that at least one is rejected

(f) Find Q₂ and Q_3, the lower and upper quartiles of the weights.