10. A normally distributed external force P ~ N(10, 0.05²) lb is applied to push a box which has a weight of 45 lb. Determine the probability that the box may tip over if the coefficient of friction between the box and floor is .

Solution

Then, we have

Also, we have

The probability that the box may tip over is

Thus, we can construct and the box might tip over when Y>0

Finally, we can obtain

Ans.