A retail company offers a scratch off promotion. Upon entering the store, you are given a...

 

Transcribed Image Text:

A retail company offers a "scratch off" promotion. Upon entering the store, you are given a card. When you pay, you may scratch off the coating. The company advertises 50% of the cards are winners and have immediate cashback savings of $5 (the others offer $1 off any future purchase of coffee in the cafe). You aren't sure the percentage is really 50% winners. Complete parts a through d below. a) The first time you shop there, you get the coffee coupon. You try again, and again get the coffee coupon. Do two failures in a row convince you that the true fraction of winners isn't 50%? Explain. V, because the chance of losing twice in a row is %, which V unusual (Type an integer or decimal.) b) You try a third time. You get coffee again! What's the probability of not getting a cash savings three times in a row if 50% of the cards really do offer cash savings? |(Type an integer or decimal.) c) Would three losses in a row convince you that the store is cheating? Since the probability of losing three times in a row is v than 0.05, this V unusual. Three losses in a row V convince me that the store is cheating. d) How many times in a row would you have to get the coffee coupon instead of cash savings to conclude that there is strong evidence that the company isn't living up to its advertised percentage of winners? Justify your answer by calculating a probability and explaining what it means. O A. Three losses in a row, the probability of getting the coffee coupon three times in a row is low enough to provide strong evidence that the percentage of winners is not 50%. O B. About 13 times in a row; if the actual percentage winners 50%, then the probability of getting the coffee coupon 13 times in a row is approximately 0.0001. O C. About 5 times in a row; if the actual percentage of winners is 50%, then the probability of getting the coffee coupon 5 times in a row is approximately 0.031. i winners is 50%, then the probability of getting the coffee coupon 10 times in a row is close to 0.001. O D. About 10 times in a row, if the actual percentage A retail company offers a "scratch off" promotion. Upon entering the store, you are given a card. When you pay, you may scratch off the coating. The company advertises 50% of the cards are winners and have immediate cashback savings of $5 (the others offer $1 off any future purchase of coffee in the cafe). You aren't sure the percentage is really 50% winners. Complete parts a through d below. a) The first time you shop there, you get the coffee coupon. You try again, and again get the coffee coupon. Do two failures in a row convince you that the true fraction of winners isn't 50%? Explain. V, because the chance of losing twice in a row is %, which V unusual (Type an integer or decimal.) b) You try a third time. You get coffee again! What's the probability of not getting a cash savings three times in a row if 50% of the cards really do offer cash savings? |(Type an integer or decimal.) c) Would three losses in a row convince you that the store is cheating? Since the probability of losing three times in a row is v than 0.05, this V unusual. Three losses in a row V convince me that the store is cheating. d) How many times in a row would you have to get the coffee coupon instead of cash savings to conclude that there is strong evidence that the company isn't living up to its advertised percentage of winners? Justify your answer by calculating a probability and explaining what it means. O A. Three losses in a row, the probability of getting the coffee coupon three times in a row is low enough to provide strong evidence that the percentage of winners is not 50%. O B. About 13 times in a row; if the actual percentage winners 50%, then the probability of getting the coffee coupon 13 times in a row is approximately 0.0001. O C. About 5 times in a row; if the actual percentage of winners is 50%, then the probability of getting the coffee coupon 5 times in a row is approximately 0.031. i winners is 50%, then the probability of getting the coffee coupon 10 times in a row is close to 0.001. O D. About 10 times in a row, if the actual percentage

Answer rating: 100% (QA)

a The two failures in a row are not convincing Reason The probability of losing t... View the full answer