16. The uniform rod AB with a length 6 ft has a normally distributed weight G ~ N(18, 0.2²) lb. (1) Determine the distribution of the force in the cable when the rod is in the position shown. (2) The maximum tension of the rod follows S ~ N(17,0.4²) lb, what is the probability the system might fail if G and S are independent?

Solution

(1)

Since the weight follows the normal distribution G ~ N(18, 0.2²) lb, we can obtain

Also, we have

Thus, we can get the force in the cable

Therefore, the force in the cable follows the distribution T ~ N(15.6, 0.39²) lb. Ans.

(2)

If the maximum load of the cable follows distribution S ~ N(17,0.4²) lb, then we can construct

Finally the probability the system may fall is

Ans.