Question: Question 1:

An industrial process makes wooden beams for the residential construction.

Answer the following questions by putting well in evidence your progress. The questions

are independent between them.

a) A beam is considered as defective when it cannot resist to a certain pressure. The industrial process is stopped and verified when a sample n = 10 beams contains more than a defective beam. In this context, which is the probability that process is stopped if it really produces 15 % of defective beams?

b) We consider that the number of breakdowns of an equipment of the manufacturer follows Poisson distribution with an average rate of two stops a day. Which is the probability that nobody stop some day? Which is the probability that there are 3 stops or more in one some day?

c) We know that the length of a wooden beam obtained with the manufacturing process is distributed according to a normal law with an average of 300 cms and 3 cm standard deviation. Standards for this stalk are 300 cms more or less 5 cms. It costs 100 $ to make

10 beams and the selling price is 22 $ the beam. If a beam is too long, it can be modified to meet the standards but in a supplementary $5 cost the beam. If beam is too small, it must be thrown. Which is the profit hoped for a manufacture of 10 000 beams with this manufacturing process?