A spring constant changes uniformly between 400 N/m and 450 N/m.

(1) Find the PDF and CDF of the spring constant.

(2) What is the probability that the spring constant is greater than 440 N/m?

(3) If the spring is stretched by 1 cm, what is the probability that the spring force is smaller than 4.3 N?

Solution

(1) PDF:
where .

CDF:

                   where .

(2)

(3)