Let X 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. 1 2 3 4 P(x) 0.2 0.3 0.4 0.1 (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 4 (b) Refer to part (a) and calculate P(X S 2.5). (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).] 1 2 P(R)
Let X 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. 1 2 3 4 P(x) 0.2 0.3 0.4 0.1 (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 4 (b) Refer to part (a) and calculate P(X S 2.5). (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).] 1 2 P(R)
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Please solve (a), (b), and (c) only!
(a) is not all 1/7
(b) is not 0.2, 0.6, or 0.4285.
(c) is not 0.25, 0.375, 0.25, and 0.125
Thank you!
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