Question

[10 marks] 6. An electronic scale in an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent. To solve each of the questions, include the following: Name and label the random variable of interest. i.e Let X = the number of . . . . . Identify its distribution with parameters using proper notation. include all the above steps will NOT receive full marks. » Show your work and then circle the final answer. Answers that do not [5m] a) What is the mean number of fills before the line is stopped? [5m] b) Four packages are inspected. What is the probability that the manufacturing line is not stopped after this inspection?

Answer 1

a) Mean number of fills = 3/0.001= 3000

b) P( not stopped in 4 ) = P( Max 2 defects in 4) =P(0)+P(1)+P(2) = 0.999^4+4*0.999^3*0.001+6*0.001^2*0.999^2=0.999999996