Problem 5 Chickenpox has predominately been eradicated in the United States due to the development of the Varicella vaccine. However, approximately 08% of infants immunized experience a serious reaction to the vaccine (febrile seizures). Suppose on a given day, one million infants are vaccinated against Chickenpox. 8) b) What is the expected number of infants that will experience febrile seizures from the Chickenpox vaccine on a given day? Be sure to justify your answer. What is the variance of the number of infants experiencing febrile seizures from the Chickenpox vaccine on a given day?I Using the dbinomO function in R, calculate the probability that exactly 850 infants develop febrile seizures after being vaccinated for Chickenpox. Is it appropriate to use the Poisson distribution in this situation [to approximate the binomial distribu tion) to model the number of serious reactions to the varicella vaccine? Explain why. What is the mean of this approximating Poisson distribution? Considering that the Poisson distribution is often used to model counts over space or time, how could you interpret the mean of the approximating Poisson distribution for this problem? Using (d), and the R function, dpoisO, determine the approximate probability that exactly 850 of the 1 million infants vaccinated against the Chickenpox experience a febrile seizure. How does this probability compare to that calculated in part (c)