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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 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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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.]
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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
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