An automobile assembly plant produces sheet metal door panels. Each panel moves

Question

An automobile assembly plant produces sheet metal door panels. Each panel moves on an assembly line. As the panel passes a robot, a mechanical arm will perform spot welding at different locations. Each location has a magnetic dot painted where the weld is to be made. The robot is programmed to locate the magnetic dot and perform the weld. However, experience shows that on each trial the robot is only 85% successful at locating the dot. If it cannot locate the magnetic dot, it is program to try again. The robot will keep trying until it finds the dot (and does the weld) or the door passes out of their robots reach.

a. what is the probability that the robots for success will be on attempts x = 1, 2, or 3?

b. The assembly line moves so fast that The robot has a maximum of only three chances before the door panel is out of reach. What is the probability that the robot will be successful before the door panel is out of reach?

c. what is the probability that the robot will not be able to locate the correct spot within three tries? If 10,000 panels are made, what is expected number of defectives?

Explanation / Answer

a) Since the robot will keep trying until it is succesful, the geometric distribution is appropriate. In this case,

success S means that the robot finds the correct location. The probability of success is p = P(S) = 0.85.

The probabilities are

n      P(n) = P(1-P)n-1 = 0.85 (1-0.85)n-1

1     0.85(1-0.85)0 = 0.85

2     0.85(1-0.85)1 = 0.1275

3     0.85(1-0.85)2 = 0.0191

(b) ince n =1 or 2 or 3 is mutually excusive, then

P(n=1 or 2 or 3) = P(1) + P(2) + P(3)

                         = 0.85 + 0.1275 + 0.0191 = 0.9966

3) The expected number of defectives is 10,000*0.9966 = 9966

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