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 60% 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.

2. Based on your table above, answer the following: Use 3-decimal precision 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?

F) What proportion of customers were satisfied and their product was delivered early?

G) What proportion of customers were not satisfied and their product was not delivered early?

H) Customer satisfaction is  --- dependent on independent of their package arriving early.

3. Which of the following are true?

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 sald they were satisfied with the product. Only 60% 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. 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 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 precision in your answers A) P(satisfied arrived early) = B) P(satisfled 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?

Answer 1

Solution :

1)

	Delivered Before Estimate
	Yes	No	Total
Satisfied	28	36	64
Not Satisfied	12	24	36
Total	40	60	100

2)

A)

$P(satisfied\: |\: arrived\: early) = \frac{P(satisfied\: and\: arrived\: early) }{P(arrived\: early)}$

$P(satisfied\: |\: arrived\: early) = \frac{28}{40} = 0.7$

B)

$P(satisfied\: \,| \:\, did\:\, not\: \,arrive\: \, early) = \frac{P(satisfied\: and\: did\: not\: arrive\: early) }{P(did\: not\: arrive\: early)}$

$P(satisfied\: \,| \:\, did\:\, not\: \,arrive\: \, early) = \frac{36}{60} = 0.6$

C)

D)

$P(\: arrived \: early \: | \: satisfied\) = \frac{P(arrived \: early \: and \: satisfied)}{P(satisfied)}$

$P(\: arrived \: early \: | \: satisfied\) = \frac{28}{64} = 0.438$

E)

$P(did\:\, not\: \,arrive\: \, early|not\,satisfied) = \frac{P(did\:\, not\: \,arrive\: \, early\: and\:not\,satisfied) }{P(not\:satisfied)}$

$P(did\:\, not\: \,arrive\: \, early|not\,satisfied) = \frac{24}{36} = 0.667$

F)

G)

H)

$Customer\:satisfaction\:\textbf{is\:dependent}\:on\:their\:package\:arriving\:only.$

3)

A majority of customers are satisfied.

Customers are about 14% more likely to be satisfied, if their package arrives early.