NBC News reported on Mag.r 2, 2013, that 11 % children in the United States have a food allergyr of some sort. Consider selecting a random sample of 22 children and let X be the number in the sample who have a food allergy. [Round your probabilities to three decimal places.) lg USES I. Selection the best answer for the following questions: (a) What is the probability distribution of X? 0 Normal with N[22, 0.11] O Binomial with ain[22, 0.11) O Poisson with Poi(22] O Exponential with Exp(22) (b) What are the possible values for X? 0 0, 1 to O 1, 2 to 22 O 1, 2 to O 0, 1 to 22 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.) I: (b) What is the probability that less than 2 children have a Food allergy? (Round your probabilities to three decimal places.) I: (c) What is the probability that exactly 2 children have a food allergy? (Round your probabilities to three decimal places.) I: (d} What is the probability that at least 3 children have a food allergy? (Round your probabilities to three decimal places.) I: (e) What is the probability that between 1 and 2, inclusive, children have a food allergy? (Round your probabilities to three decimal places} I: (f) Calculate the expected value and standard deviation of X. (Round your standard deviation to two decimal places.) expected value standard deviation