24. A ball with a weight of m ~ N(10, 0.02²) kg is placed between the 45° grooves A and B of the 20° incline. Determine the probability that the external force P ~ N(7.8, 0.05²) N which is independent from m may hold the ball up from slipping if the coefficient of friction between the ball and groove is .

Solution

Also, we have

Then, we can obtain

Thus, we have

Also, along x axis we have

The probability that external force P can hold the ball is that P should satisfy the above inequality, therefore we construct

Finally, the probability that the external force P can hold the ball is

Ans.