In a study to reveal the relation between IQ and depression, it was established that 25% of the adult population suffers from depration and those who are depressed have an average IQ of 105 which is normally distributed with a standard deviation of 15 points. 

(a) If a random sample of 60 persons from the population is picked, what is the probability that at least 24 of them suffer from depression? 

(b) If a random sample of 10 persons is picked, what is the probability that at most, only 1 of them suffers from depression? 

(c) If a random sample of 100 depressed individuals is picked, what is the probability that their average IQ is more than 110? 

(d) If a random sample of 10 depressed individuals is picked, what is the probability that their average IQ is more than 110? 

(e) If we pick a random individual from the population, what is the probability that this individual will be a patient of depression with an IQ higher than 115?