Question

Q27 A manufacturing plant’s main production line breaks down an average of 2.4 times per day. Whenever the line goes down, it costs the company $500 in maintenance, repairs, and lost production. What is the probability that the production line will break down at least 3 times tomorrow? What is the approximate expected value for the amount of money that production line breakdowns will cost the company each day? [2 Marks]

DO NOT WRITE THE ANSE - USE WORD FORMAT

Answer 1

Let X = number of main production line breaks down per day.

So X follows Poisson distribution with mean = = 2.4

Here we want to find P( X >= 3 ) = 1 - P( X < 3) = 1 - P( X <= 2) .....( 1)

Let's use excel:

P( X <= 2) = "=POISSON(2,2.4,1)" = 0.5697

Plug this in equation ( 1 ), we get

P( X >= 3 ) = 1 - 0.5697 = 0.4303

Next we want to find the expected amount.

Expected amount = 500*2.4 = 1200

So the approximate expected value for the amount of money that production line breakdowns will cost the company each day is $200