2. Suppose that the weights of 5-year-old boys in a certain area are normally distributed, with a mean of 19.5 kg and a standard deviation of 2.3 kg. A 5-year-old boy is randomly selected from this area and his weight is measured. Answer the following questions:

(a) What is the probability that his weight is less than 16.1 kg?

(b) What is the probability that his weight is more than 22.9 kg?

(c) What is the probability that his weight is between 16.1 kg and 22.9 kg?

(d) Determine the smallest x such that the probability that his weight is more than x is 0.05.

(e) If three 5-year-old boys are selected simultaneously, what is the probability that they all weigh less than 16.1 kg?

(f) Following (c), what is the probability of at least one in three 5-year-old boys weighing more than 22.9 kg?
(g) If two 5-year-old boys are selected successively and the first boy weighs less than 16.1 kg, what is the probability that the second boy also weighs less than 16.1 kg?