2. 1) A table has a weight of 55 lb with its center of gravity at . A crate with a weight of is put in the position shown, and the center of gravity is . To keep the table from tipping over, what is the largest weight of the crate?

2) After the measurement of several crates, is known to follow a normal distribution , and due to manufacturing imprecision, also follows a normal distribution . What is the probability that the table will tip over? and are independently distributed.

Solution

1)

We suppose; this is the minimum vertical reaction force required to keep the table from tipping over. . From above equation,

Ans.

2)

We know and , so we can find and

If the table will tip over, . The probability is

Ans.