The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Based on these data,if a board is selected that is 12 feet long,the probability that it was made at sawmill A is:
A)0.08.
B)0.41.
C)0.24.
D)0.20.

Question

The Anderson Lumber Company has three sawmills that produce boards of different lengths.The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory.  Based on these data,if a board is selected that is 12 feet long,the probability that it was made at sawmill A is:
A)0.08. 
B)0.41. 
C)0.24. 
D)0.20.

Quizplus · Accepted Answer

The probability that a board is 12 feet long is (34+60+106)/1000 = 0.2. 
The probability that a 12-foot board was made at sawmill A is 34/200 = 0.17.
The probability that a 12-foot board was made at sawmill B is 60/200 = 0.30.
The probability that a 12-foot board was made at sawmill C is 106/200 = 0.53.
Therefore, the best choice is B, as sawmill B has the highest probability of producing a 12-foot board.

The Anderson Lumber Company Has Three Sawmills That Produce Boards