Please assist and please show R code

What proportion of residents of New York City are vaccinated against covid-19? Because of double counting, lack of counting, poor procedures, lack of unied database, etc. it is not as easy a question as it might seem. However, NYC has an accurate database {Call it DB.) of all residents. [This is not actually true, but we will assume it.). Researchers at HJH took a random sample of n=4111 New York City residents from DB. of these, x = 18?1 residents were vaccinated against Covid 19. Let p be the {unknown} true proportion of New York City residents vaccinated against Covid19. We want to estimate p. x is the random variable representing the number of sampled NYC residents who were vaccinated. a) What type of probability distribution does K have? 0 gamma 0 exponential O Weibull O Poisson O binomial b} What was the sample proportion, f), of sampled residents who were vaccinated? \\:| c} What is the R formula for the expected value of X in terms of n and p? O sqrtln*p*{1-p)} O nA2 O n*p*[1 - p} O lip O n'p d} what is the 2 critical value that we would use to construct a classical 91% confidence interval for p? :l | l e) Construct a 91% classical confidence interval for p? [I f} How long is the 91% classical condence interval for p'? E g} If we are creating a 91% classical condence interval for p based upon the sample size of 4111, then what is the longest possible length of this interval? :| h} Copy your R script for the above into the text box here