Three businesses in a suburb responded to a questionnaire asking how many people
ID: 3366061 • Letter: T
Question
Three businesses in a suburb responded to a questionnaire asking how many people paid for their purchases last month using cash, credit cards, and debit cards. A customer who makes a purchase is selected randomly from the sample summarized in the table. Use this information to answer the first 9 questions.
Round your final answers to the nearest thousandth.
Payment Method
Beth’s Coffee House
Michael’s PC Repair and Sales
John’s Medical Supply
Total
Cash
304
140
23
467
Debit Card
456
166
219
841
Credit Card
380
257
102
739
Total
1140
563
344
2047
8. Determine if the event that a customer selected at random used a debit card and the event that they shopped at Michael’s PC Repair and Sales are independent using the methods as shown in the video presentations from the Study Help area of Blackboard.
9. How would the probability that a randomly selected customer used credit card and shopped at Beth’s Coffee House compare with the probability that a randomly selected used a credit card and shopped at John’s Medical Supply?
Payment Method
Beth’s Coffee House
Michael’s PC Repair and Sales
John’s Medical Supply
Total
Cash
304
140
23
467
Debit Card
456
166
219
841
Credit Card
380
257
102
739
Total
1140
563
344
2047
Explanation / Answer
8) P(Debit card AND Michael's PC Repair) = P(Debit card | Michael's PC Repair) / P(Michael's PC Repair)
P(Michael's PC Repair) = 563 / 2047
P(Debit card | Michael's PC Repair) = 166 / 563
P(Debit card AND Michael's PC Repair) = 166 / 563 * 563 / 2047 = 166 / 2047
9) P( Credit Card AND Beth'sCoffee) = P(Credit Card | Beth's Coffee) * P(Beth's Coffee)
P(Credit Card | Beth's Coffee) = 380 /1140
P(Beth's Coffee) = 1140/2047
P( Credit Card AND Beth'sCoffee) = 380 / 2047 =0.185638
P(Credit Card AND John's Medical) = P(Credit Card | John's Medical) * P( John's Medical)
P(Credit Card | John's Medical) = 102/344
P( John's Medical) =344/2047
P(Credit Card AND John's Medical) = 102/344* 344/2047 = 0.049829
The credit card probability usage at Beth's house(0.185638) comparatively higher than John's medical supply(0.049829).
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