Question

The main production line in a manufacturing plant runs 24 hours a day and breaks down on average 2.6 times in a working week of 7 days. It is known that the number of breakdowns has a Poisson distribution.
i. What is the probability that the production line breaks down three (3) times in one working week?   

ii. What is the probability that the production line breaks down one (1) or more times in two working weeks?   

Answer 1

Average breakdowns in a working week is 2.6 times

Thus, = 2.6/ working week

Let X be the number of breakdown

a) P( X= 3) = = = 0.2176

b) Here = 2.6 * 2 per 2 working weels

= 5.2 per two working week

P( X>=1 ) = 1- P( X <1)

= 1- P( X=0)

= 1-

= 1- 0.0055

= 0.9945