14. A random force P ~ N(40,5²) lb is applied to push a cart with wheels with a radius of in. The weight of the cart is also a random variable W ~ N(1000,20²) lb and is independent of P. Given the coefficient of rolling resistance in, determine the probability that the cart will start to move.

Solution

Then, we have

Also, the rolling resistance is

The probability that the force P can overcome the resistance is, where

Therefore, we can obtain

Finally, the probability that the force P can pull the cart is

Ans.