Suppose that for a given computer salesperson, the probability distribution of X = the number of systems sold in one week is given by the following table. x 1 2 3 4 5 6 7 8 p(X) 0.04 0.10 0.13 0.30 0.29 0.12 0.01 0.01 (a) Find the mean value ofX (the mean number of systems sold}. / (b) Find the variance and standard deviation of X. (Round your standard deviation to four decimal places.) variance 1.8875 / standard deviation 1.3738 3.; How would you interpret these values? (Round your standard deviation to four decimal places.) The mean squared deviation from the mean number of systems sold in one week is 1.8875 / . Atypical deviation from the mean number of systems sold in one week is 1.3738 x (c) What is the probability that the number of systems sold is within 1 standard deviation of its mean value? / (d) What is the probability that the number of systems sold is more than 2 standard deviations from the mean? x NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 20 children and let X be the number in the sample who have a food allergy. Then X N Bin(20, 0.05}. (Round your probabilities to three decimal places.) IQ use SALT (a) Determine both P(X s 4) and P(X a 4). ear: 4} = 0.997426 \\y P(X