NBC News reported on Magir 2, 2013r that 12 % children in the United States have a food allergyr of some sort. Consider selecting a random sample of 39 children and let X be the number in the sample who have a food allergy. [Round your probabilities to three decimal places.) lg USE SALT I. Selection the best answer for the following questions: (a) What is the probability distribution of X? 0 Exponential with Exp(39) O Poisson with Poi(39] O Normal with was, 0.12) O Binomial with Bin[39, 0.12] (b) What are the possible values for X? O 1, 2 to 40 O o, 1 to as O o, 1 to 39 O 1, 2 to 39 II. Calculate the probabilities: (a) What is the probability that at most 2 children have a food allergy? (Round your probabilities to three decimal places} E {b} What is the probability that less than 2 children have a food allergy? [Round your probabilities to three decimal places.) E (c) What is the probability that exactly 2 children have a food allergy? (Round your probabilities to three decimal places.) E (d) What is the probability that at least 3 children have a food allergy? (Round your probabilities to three decimal places.) [f] Calculate the expected value and standard deviation of X. (Round your standard deviation to two decimal places.) standarddeviation \\:|