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 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 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 probabilities from part (a).] R 1 2
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 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 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 probabilities from part (a).] R 1 2
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 the screenshot, (a) and (b) only. The answer for (b) is not 0.2!
![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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32f563a-6b55-4123-a4c3-1254c39a7403%2Fdfec449d-fd5d-419b-bd89-8ae933a57576%2F8l7cp3c_processed.png&w=3840&q=75)
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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