et 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. 1.5 2 2.5 3 3.5 P(X) (b) Refer to part (a) and calculate P(X S 2.5).
et 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. 1.5 2 2.5 3 3.5 P(X) (b) Refer to part (a) and calculate P(X S 2.5).
Please solve (a) and (b) only! The answer for (b) is not 0.2 or 0.6!
Transcribed Image Text: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
P(x)
(b) Refer to part (a) and calculate P(X S 2.5).
(c) Again consider a random sample of sizen = 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)
(d) If a random sample of size n = 4 is selected, what is P(X S 1.5)? [Hint: You should not have to list all possible outcomes, only those for which xS 1.5.]
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![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
P(x)
(b) Refer to part (a) and calculate P(X S 2.5).
(c) Again consider a random sample of sizen = 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)
(d) If a random sample of size n = 4 is selected, what is P(X S 1.5)? [Hint: You should not have to list all possible outcomes, only those for which xS 1.5.]](https://content.bartleby.com/qna-images/question/306db17a-c2a3-4020-aada-7a92dff91485/4d5990ab-f8f6-43d3-9ace-e5ed48d8e20e/fo6ejll_processed.png)
