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Let be the number of packages being mailed by a randomly selected customer at a...

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Let be the number of packages being mailed by a randomly selected customer at a certain shipping facility Suppose the distribution of X is as follows 2 3 4 p x 0 2 0 4 0 1 0 3 X X a Consider a random sample of size n 2 two customers and let X be the sample mean number of packages shipped Obtain the probability distribution of X 1 1 5 2 2 5 3 3 5 P X 0 04 1 0 6 0 16 b Refer to part a and calculate P X 2 5 0 3 0 2 0 28 0 2 2 c Again consider a random sample of size n 2 but now focus on the statistic R the sample range difference between the largest and smallest values in the sample Obtain the distribution of R Hint Calculate the value of R for each outcome and use the probabilities from part a R 0 1 3 P R 0 3 0 25 0 12 0 06 0 09 4 d If a random sample of size n 4 is selected what is P X 1 5 Hint You should not have to list all possible outcomes only those for which x 1 5

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