Please answer the following using code with R. Functions taught this class were dbinom, pbinom, pnbinom, dpois, ppois, pnorm, qnorm

# Question 1 # A researcher in 2022 was attempting to measure the rate of long-COVID # in the population. Unbeknownst to the researcher, approximately 6.9% # of the population experienced long-COVID symptoms in 2022. During one # of their shifts they have time to call and survey 220 people.

# Question 1.e # What is the probability that the researcher has to make more calls than # they would expect? (Reminder that R only counts 'failures') # Save your answer in the variable q1.e q1.e<-NA

# Question 2 # In America, a criminal trial jury maintains the right of jury nullification, # declaring not-guilty despite evidence to the contrary due to disagreements # with the law being applied in the case. It is estimated that approximately # 21% of acquittals (declarations of not-guilty) are the result # of jury nullification.

# Question 2.b # What is the probability that at least the next 5 acquittals are not the # result of jury nullification? # Save your answer in the variable q2.b q2.b<-NA

# Question 2.c # How many acquittals should the prosecutor expect in total to observe # the 4th jury nullification acquittal? # Save your answer in the variable q2.c q2.c<-NA

# Question 2.d # What is the probability that the prosecutor sees the 4th jury nullification # before the 15th acquittal? # Save your answer in the variable q2.d q2.d<- NA