A survey shows that about 10% of those over the age of 65 years old are in danger of catching COVlD-19. If 12 persons over the age of 65 are randomly selected (assuming a binomial distribution}, answer the following questions: Round all final answers to 3 decimal places and express answers in decimal form (i.e. 0.003 instead of 0.300%) (a) What is the probabilitiy that exactly 3 have COVlD-19? :J (b) What is the probability that at most 3 have COVlD-19? : (c) What is the probability that at least 1 has COVlD19? :] (d) What is the probability that between at least 1 and no more than 4 have COVlD-19? :] Suppose approximately 40% of all students study after midnight. For random sample of n = 3 students, let X be the number of students that study after midnight. a. Complete the following table for the binomial distribution of X. Keep at least 4 decimal places. X P(X) 0 1 2 3 Determine the mean and standard deviation of X. Keep at least 4 decimal places. b. The expected value of X = c. The standard deviation of X