5. The weight of the platform assembly follows a normal distribution . The center of gravity of the platform is at . The counterweight at A is used to prevent the platform from tippling over, and its distribution is . If the load at point is 390 lb, what is the probability that the platform will tip over? and are independently distributed.

Solution

When tipping occurs,

From above equation, we have

Given, and they are distributed independently, and are calculated by

Thus, we get

If the platform will tip over, will be greater than the maximum load 390 lb at point , Suppose

We can calculate and by

Thus the probability that the platform will tip over is

Ans.