Question

Data from the past shows that on average, a ready-mixed concrete plant receives 100 orders for concrete every year. The maximum number of orders that the plant can fulfill each week is 2. (a) What is the probability that in a given week the plant cannot fulfill all the placed orders? (b) Assume the answer to part (a) is 20%. Suppose there are 5 of such plants. What is the probability that in a given week 2 of the plants cannot fulfill their orders?

Answer 1

Average total number of orders per year=100

Number of weeks in a normal year =52

so

Average order per week =100/52 =1.92

X is number of orders per week Hence  X can be assumed to be Poisson with lambda=average =1.92 therefore

a)

As plant can fulfill maximum upto 2 orders per week hence  if there are more than 2 orders in a given week then plant can not  fulfill the order Therefore  we need to find P(X>2)

now

b)

P(not fulfilling the order in a week )=p=0.2 (given)

t n=5 plants and each has an equal probability of not able to fulfill the orders in a given week

let Y is the number of plants out of 5 plants that are not able to fulfill the order in a given week so

Y is a binomial distribution with n=5 p=0.2 so

now we to find P(Y=2)

Therefore answer isgiven by

We were unable to transcribe this image