A spring constant changes uniformly between 500 N/m and 550 N/m.

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

(2) What is the probability that the spring constant is greater than 540 N/m?

(3) If the spring is stretched by 1 cm, what is the probability that the spring force is smaller than 5.3 N?

Solution

(1)  Let X be the spring constant, , and  . The PDF of the spring constant is

where .

The CDF of the spring constant is

where .

(2) The probability that the spring constant is greater than 540 N/m is calculated by

(3) If the spring is stretched by 1 cm, the spring force is equal to . The probability that the spring force is smaller than 5.3 N is