Q1) Cereal manufacturer is aware that weight of product in box varies slightly from box to box. Actually, considerable historical data has allowed determination of density function which explains probability structure for weight (in ounces).  In fact, letting X be random variable weight, in ounces, density function can be explains as

f(x) =  2/5,             23.75 ≤ x ≤ 26.25,

0, elsewhere.

i) Verify that this is valid density function.

ii) Find out probability that weight is smaller than 24 ounces.

iii) The company wishes that weight exceeding 26 ounces is extremely rare occurrence. Determine the probability that this "rare occurrence" does actually occur?