Let X be the number of packages being malled by a randomly selected customer at a certain shipping facility Suppose the 2 3 1 p x 0 1 0 2 0 3 0 4 X PX 4 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 2 5 3 1 5 3 5 4 1 b Refer to part a and calculate P X 2 5 2 c Again copsider 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 distributic R Hint Calculate the value of R for each outcome and use the probabilities from part a 2 R 1 3 0 P R 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