A company sends packages to a particular customer in one of three ways: Regular

Question

A company sends packages to a particular customer in one of three ways: Regular delivery, priority, and expedited. When an employee sends a package to the mail room it is believed that there is a 42% chance it will be a regular delivery, 37% chance it will be priority, and 21% chance it will be expedited. The delivery methods have the following distribution of delivery times (in photo) A company sends packages to a particular customer in one of three ways: Regular delivery, Priority delivery, and Expedited delivery. When an employee sends a package to the mail room, it is believed that there is a 42% chance that it will be a Regular deliver, a 37% chance that it will be a Priority delivery, and a 21% chance that it will be an Expedited delivery. It is also believed that the delivery methods have the following distribution of delivery times: 0-33 6.21 Delivery Time Regular Delivery Priority Delivery Expedited Delivery 1 day 0.7 0.3 0.1 0.2 0.3 0.4 0.4 0.4 0.2 2 days 3 days 4 days What is the expected delivery time for an arbitrary package? What is the probability that Priority Mail was used, given that the package was delivered in one day? Are the events "Priority Delivery" and "3 days" dependent or independent? a) b) c)

Explanation / Answer

a) Expected Delivery Time (Overall) = ??

Expected Delivery Time (EDT) for Regular Delivery = Delivery Time(Regular) * Probabilities = 1*0.1 + 2*0.2 + 3*0.3 + 4*0.4 = 3 days

EDT for Prioirity Delivery = 1*0.4 + 2*0.4 + 3*0.2 = 1.8 days

EDT for Expedited Delivery = 1*0.7 + 2*0.3 = 1.3 days

Overall EDT = 3*0.42 + 1.8*0.37 + 1.3*0.21 = 2.199 days

b) Given -- That package was delivered in 1 day.

Probability that it was a Priority Package = (0.37*0.4) / [0.1*0.42 + 0.37*0.4 + 0.21*0.7] = 0.148/0.337 = 0.44

c) Yes, they are dependent events as we can see in Part b.

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