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 80% of those whose product arrived ahead of the estimated delivery date said they were satisfied with the product. Only 50% whose product did not arrive ahead of the estimated date said they were satisfied. Overall, 40% of packages arrived ahead of the estimated delivery date.

1. Based on this survey, fill out two-way table below with the number of people in each cell. For each blank spot in the table below you have 5 attempts.

	Delivered Before Estimated Date
.	Yes	No	Total
Satisfied
Not Satisfied
Total			100

You should submit your answers above to make sure they are correct before trying the remaining questions. Remember that any questions that are unanswered will not be graded.

2. Based on your table above, answer the following: Use 3-decimal places in your answers

A) P(satisfied | arrived early) =

B) P(satisfied | did not arrive early) =

C) P(satisfied) =

D) P(arrived early| satisfied)

E) What is the probability that a package did not arrive early given that the customer was not satisfied?
You may want to submit your answers above before trying the remaining questions.

F) Customer satisfaction is  --- dependent on independent of their package arriving early. One attempt.


3. Which of the following are true? You have 5 attempts and must answer all correct.

Customers are less likely to be satisfied if their package arrives early rather than not early.

Customers are more likely to be satisfied if their package arrives early rather than not early.

A majority of customers are satisfied.

Customers are equally likely to be satisfied if their package arrives early or not early.

A majority of customers' packages arrive early.

Answer 1

1) They randomly survey 100 customers. They found that 80% of those whose product arrived ahead of the estimated delivery date said they were satisfied with the product. Only 50% whose product did not arrive ahead of the estimated date said they were satisfied. Overall, 40% of packages arrived ahead of the estimated delivery date.

Delivered before estimated date

	Yes	No	Total
Satisfied	32	30	62
Not satisfied	8	30	38
Total	40	60	100

2)

A) P(satisfied | arrived early) = P( satisfied and early arrived) / P(early arrived)

= 0.32 / 0.40 = 0.800

B) P(satisfied | did not arrive early)

= P( satisfied and did not arrived early) / P(did not arrived early)
= 0.30 / 0.60

= 0.500
C) P(satisfied) = 62/100 = 0.620

D) P(arrived early| satisfied) = P(satisfied and early arrived) / P(satisfied)

= 0.32 / 0.62 = 0.520

E) P( did not arrive early | Not satisfied)

= P(not satisfied and did not arrived early) / P(not satisfied)

= 0.30 / 0.38 = 0.789

F) Customer satisfaction is dependent on their package arriving early.

as, P(satisfied and arrived early) = 0.32 P(satisfied)*P(arrived early) = 0.62*0.40 = 0.25

3)

Customers are less likely to be satisfied if their package arrives early rather than not early. False

Customers are more likely to be satisfied if their package arrives early rather than not early. True

A majority of customers are satisfied. True

Customers are equally likely to be satisfied if their package arrives early or not early. False

A majority of customers' packages arrive early. False.

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