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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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
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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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F306db17a-c2a3-4020-aada-7a92dff91485%2F538bf9da-6d6b-420d-be98-e4babbaeae80%2Frpjeuj_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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