Please answer all shown parts of each question. Please show all work and explanations where needed. Thanks!

Between juiy 27. 2020, and November 14. 2020. a total of 44,820 persons were screened. and 43,548 persons 16 years of age or older undemnt randomization at 152 sites woridwide (United States. 130 sites; Argentina. 1: Brazil, 2; South Africa. 4: Germany. 6; and Turkey. 9) In the phase 2/3 portion of the trial. A total of 43.448 participants received Injections: 21.720 received BNTi SIM and 21.728 received placebo. Not all participants ended up in the study. Among 36,523 participants who had no evidence of existing or prior SARS-CoV-z Infection. 8 cases of Covidi 9 with onset at least 7 days after the second dose were observed among vaccine recipients and 162 among placebo recipients. The exact number of the vaccinated participants who were observed at least 7 days alter the second dose of the vaccine was 18.198. while the number of the placebo group (they received fake vaccines) was 18,325. Find the 95% condence intervals for the me of infections resulting from each group at least 7 days atter the second dose was administered to the test group. A certain type of tennis racket comes In midsize and oversize versions. The store has "I rackets of the oversize version and 8 of the midsize. Seventeen customers in a three-day period arriving at the store individually from each other. request 5 oversize and 12 midsize rackets. None of them buys two or more rackets. Can we conclude maino more than 40% of the customers prefer to buy an oversize racket? Using this information, what would be a reasonable number of oversize rackets to stock the more is going to order 33 rackets? DO NOT FORGET toJUSTIFY YOUR ANSWERS IN ALL OF THE ABOVE PROBLEMS