Reference no: EM132361869

There are a number of companies that provide a delivery service for take away meals. One of the important factors for the customer is the time between placing an order and receiving the meal. A particular Thai restaurant use two different delivery companies. Company A delivers 40% of their orders while Company B delivers the rest. A survey of customers using the service have indicated they want their food delivered within 30 minutes. Historically, Company B has experienced 10% of their orders taking longer than 30 minutes to deliver while Company A has been late on 15% of their orders.

a. We will use A to represent the event 'Company A delivers the order' and L to represent the event 'The meal is delivered late'. Use the correct statistical notation and words to define the complement of both A and L. (Use this terminology in your working throughout the remainder of this question).

b. Construct a fully labelled probability tree to describe this problem with the outcomes and probabilities shown along each branch.

c. A customer has just received their order. What is the probability the order was delivered on time, that is, within 30 minutes of placing the order?

d. A customer who contacted the Thai restaurant reported receiving their order 45 minutes after placing the order. Which company is most likely to have delivered the order? Use probabilities to support your conclusion.

e. Considering the probability calculated in part c., should the restaurant owner have any concerns about the reliability (delivery times) of the delivery companies they use? Explain.