NBC News reported on May 2, 2013, that 11 % children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. ( places.) USE SALT I. Selection the best answer for the following questions: (a) What is the probability distribution of X? Poisson with Poi(15) Normal with N(15, 0.11) Binomial with Bin(15, 0.11) Exponential with Exp(15) (b) What are the possible values for X? 0,1 to 14 1, 2 to 16 0, 1 to 15 1, 2 to 15 II. Calculate the probabilities: (a) What is the probability that at most 3 children have a food allergy? (Round your probabilities to three decimal places.) 884 (b) What is the probability that less than 3 children have a food allergy? (Round your probabilities to three decimal places.) (c) What is the probability that exactly 3 children have a food allergy? (Round your probabilities to three decimal places.) 247 x (d) What is the probability that at least 4 children have a food allergy? (Round your probabilities to three decimal places.) (e) What is the probability that between 1 and 3, inclusive, children have a food allergy? (Round your probabilities to three decimal places.)