When a retailer places an order with an overseas supplier, the product takes an average of 100 days to arrive with a standard deviation of 20 days. Orders from a local supplier take an average of 80 days with a standard deviation of 40 days. Delivery times in both cases are normal random variables.

Assume that delivery times from the two suppliers are independent.

a. What is the probability that an order placed with the overseas supplier arrives within 80 days?

b. When the retailer places an order for product that is needed by a certain date, its goal is to order as late as possible but still be 90% sure that the product will arrive by the due date. With this goal, which supplier would be better to use? Explain briefly.

c. It has been 120 days since an order was placed with the local supplier. What is the probability that the product will arrive in the next 40 days?

d. Suppose that the retailer places orders with both the local and the overseas supplier today.

i. What is the probability that neither order is delivered 100 days from today?

ii. What is the probability that the order from the local supplier arrives before the order

from the overseas supplier?