11. The weight follows a normal distribution . The resistances of cable AC and cable AB are also normally distributed with and , respectively. Determine which cable is more likely to break. , , and are independent.

Solution

For cable AC

We construct the function

The probability that cable AC will break is

For cable BC

We construct the function

The probability that cable BC will break is

We can see

Thus, cable AC is more likely to break. Ans.