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 fulfil each week is 2. (a) What is the probability that in a given week the plant cannot fulfil all the placed orders? (b) Assume the answer to part (a) is 20% (It is not; I just want to make sure that everybody uses the same number for part (b)). 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

Given 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 fulfil each week is 2.

In a year there are 52 weeks i.e.they can supply 104 orders ie it is assume that, all working days in a year.  

P(A) =The probability of fulfilling each week is 2/7 = 0.29

(a) The probability that in a given week the plant cannot fulfil all the placed orders = 1-P(A) = 5/7= 0.71

(b) Assume the answer to part (a) is 20% (It is not (b))

Suppose there are 5 of such plants. then, the probability that in a given week 2 of the plants cannot fulfill their orders is =0.14