Question

An online retailer is studying product reviews and wants to see if customer satisfaction and timeliness of delivery are related. They randomly survey 100 customers. They found that 70% of those whose product arrived ahead of the estimated delivery date said they were satisfied with the product. Only 10% whose product did not arrive ahead of the estimated date said they were satisfied. Overall, 80% of packages arrived ahead of the estimated delivery date. For each blank below you have 5 attempts. 1. Based on this survey, fill out two-way table below with the number of people in each cell Delivered Before Estimated Date Yes 70 No X10 X10 20 Total Satisfied Not Satisfied 10 Total X80 20 80 100 2. Based on your table above, answer the following: Use 3-decimal precision in your answers A) P(satisfied | arrived early)875 B) P(satisfied | did not arrive early)50 C) P(satisfied)8 D) P(arrived earlyl satisfied) 1 E) What is the probability that a package did not arrive early given that the customer was not satisfied? .50 F) What is the probability that a customers was satisfied and their product was delivered early? 1 G) What is the probability that a customers was not satisfied and their product was not delivered early? 1

Answer 1

1.

Customers surveyed = 100

No of. Packages arrived before the estimated delivery date = 80% of 100 = 80 packages for 80 customers

No. of packages that didn't arrive early = 100-80 = 20

70% of people whose package arrived early were satisfied = 70%of 80 = 56 customers

No of customers whose package arrived early but they were not satisfied = 80 - 56 = 24

10% of people whose product didn't arrive early but they were still satisfied = 10% of 20 = 2 customers

	Delivered Before Estimate
	Yes	No	Total
Satisfied	56	2	58
Not Satisfied	24	18	42
Total	80	20	100

2. Conditional Probability

"Probability Of "Given" Pl A and B ) = P(A ) x P(B | AJ Event A Event B "Probability of event A and event B equals the probability of event A times the probability of event B given event A"

A) P (satisfied| Arrived Early ) = P (Satisfied and Arrived Early) / P (Arrived Early) = 0.56 / 0.8 = 0.7

B) P (satisfied| Didn't Arrive Early ) = P (Satisfied and Didn't Arrive Early) / P (Didn't Arrive Early) = 0.02 / 0.2 = 0.1

C) P(satisfied) = 0.58

D) P(arrived Early | Satisfied ) = P (Satisfied and Arrived Early) / P (Satisfied) = 0.56/ 0.58 = 0.96

E) P ( Didn't Arrive Early| Not satisfied ) = P (Not Satisfied and Didn't Arrive Early) / P (Not satisfied) = 0.18/ 0.42 = 0.42

F) P (Satisfied and Arrived Early) = 0.56

G) P (Not Satisfied and Didn't Arrive Early) = 0.18