11. The block which has a normally distributed weight m ~ N(10, 0.05²) kg is being pulled up the inclined plane of slope α using another independent normally distributed external force P ~ N(100, 1.5²) N. Determine the probability that the external force P can pull the block up if the coefficient of friction is .

Solution

And, we have

Then, we can obtain

If P is sufficiently large to pull the block up, then we have

Therefore, we can define

Thus, we can obtain

Finally, we can calculate the probability that the force P can pull the block up is

Ans.