This is the question for AP Statistics Unit 5. Answer the question using appropriate subject vocabulary and information based on the question. The question is: A caf advertises a promotion during a certain week. They claim that during the promotion week 20% of the members in their loyalty program will be emailed a coupon for a free cookie. A group of 12 friends are all members of this caf's loyalty program. During the week of this promotion, only 1 of the 12 friends received the email with the coupon. ( 1 ) If the caf's claim is true, how many of the friends would you expect to have received the coupon? Justify your answer. ( 2 ) Is there some evidence that the caf's claim is false? Explain. ( 3 ) A simulation is done to determine the probability of getting a result like this, purely by chance. The dotplot displays the results of 50 simulated trials. Each dot represents the number of coupon recipients in a group of 12, if the probability of winning was truly 20%. How many of the 50 simulated trials included 1 or fewer coupon recipients? ( 4 ) Assuming the caf's claim is true, what is the approximate probability of getting 1 or fewer coupon recipients in a group of 12? ( 5 ) Is there convincing evidence that the caf's claim is false? Explain