Question

Changeovers take place on a bottling line at a popular dairy to ensure that there is no cross-contamination of different milk products.

70% of all changeovers occurred during the first shift, 20% of the changeovers occur during the second shift, and the remaining 10% changeovers occur during the third shift.

Because of differences in training, the average time to execute a changeover varies from shift to shift 15, 25, and 30 minutes for shift one, two and three.

a. What is the expected time it takes for the changeover at the dairy

b. what can we say about the probability that a changeover on shift 1 takes more than 45 minutes?

Answer 1

a)

expected time it takes for the changeover E(changeover) =P(first shift)*E(changeover |first shift)+P(2nd shift)*E(changeover |2nd shift)+P(3rd shift)*E(changeover |3rd shift)

=0.7*15+0.2*25+0.1*30

=18.5

b)

we can assume that changeover time on shift 1 follows exponential distribution with parameter =15

probability that a changeover on shift 1 takes more than 45 minute =P(X>45)=e^-45/15 =0.0498