5. (10 points) Acute rotavirus diarrhea is the leading cause of death among children under age...
5. (10 points) Acute rotavirus diarrhea is the leading cause of death among children under age 5, killing an estimated 4.5 million annually in developing countries. Scientists from Finland and Belgium claim that a new oral vaccine is 80% effective against rotavirus diarrhea. a) What is the probability distribution of the random variable X, the number of effective cases out of 1500 cases? b) What is the probability that the vaccine will be effective in less than 1225 cases? c) What is the probability that the vaccine will be effective in At least 1175 cases? d) What is the probability that the vaccine will be effective between 1150 and 1250 cases, inclusive? e) Find the mean and standard deviation of X. f) Use the normal approximation to the binomial distribution to redo parts b)-d). Are the answers in this part close to what you obtained in previous parts?