4-6. A company makes garage doors as shown in the figure. The garage door is pulled by a rope with a constant force F that will move the door horizontally a distance to the right. is a random variable that follows a normal distribution. The distances of a number of operations are measured in 4 seconds, and this results in a distribution . The door has a mass of 20 kg and does not touch the ground by hanging from two rollers, A and B. Find the force F and the vertical reaction forces at the rollers.

Solution:

Thus,

Therefore ; ; . Ans.