3.2 Assume that scores from an I.Q. test follow a Gaussian distribution, and that the scores are standardized in such a way that the mean is  D 100, and the standard deviation is  D 15.

(a) Calculate the probability that an I.Q. score is greater or equal than 145.

(b) Calculate the probability that the mean I.Q. score of a sample of 100 persons, chosen at random, is equal or larger than 105.