Please include the R Script :) Will rate the response!

Covid-19 can be devastating. Researchers at ] Health Services took a random sample of n=3947 hospitalized Covid-19 patients out of a very large population of hospitalized Covid-19 patients. Of these, x = 2903 patients showed a symptom of loss of smell (LOS). Let p be the (unknown) true proportion of Covid-19 patients who show a symptom of LOS. We want to estimate p. X is the random variable representing the number of sampled Covid-19 patients with LOS? a) What type of probability distribution does X have? O binomial O Weibull O Poisson O gamma exponential b) What was the sample proportion, p, of sampled patients with symptoms of LOS? c) What is the R formula for the expected value of X in terms of n and p? O sqrt(n*p*(1-0)) O n*p*(1-P) 0 1/p 0 n^2 O nap d) What is the z critical value that we would use to construct a classical 94% confidence interval for p? e) Construct a 94% classical confidence interval for p? ( f) How long is the 94% classical confidence interval for p? g) If we are creating a 94% classical confidence interval for p based upon the sample size of 3947, then what is the longest possible length of this interval